By resorting to recent results on fermion mixing which show that the Fock space of definite flavo... more By resorting to recent results on fermion mixing which show that the Fock space of definite flavor states is unitarily inequivalent to the Fock space of definite mass states, we discuss the phenomenological implications on the neutrino oscillation formula. For finite momentum the oscillation amplitude is depressed, or "squeezed", by a momentum dependent factor. In the relativistic limit the conventional oscillation formula is recovered.
We discuss some recent results on neutrino physics in the context of the inverse β-decay of unifo... more We discuss some recent results on neutrino physics in the context of the inverse β-decay of uniformly accelerated protons. Specifically, we compute the decay rate of the process p → n + e + + ν in both the laboratory frame (where the proton is non-inertial) and the comoving frame (where the proton is at rest and interacts with a thermal bath of electrons and neutrinos due to the Unruh effect). On the basis of the sole requirement of General Covariance of Quantum Field Theory, we manage to show that: i) the asymptotic (i.e. “in” and “out” ) neutrino states to be used for the evaluation of the S-matrix are Pontecorvo flavor eigenstates, ii) the Unruh thermal bath must be made up of oscillating neutrinos.
Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017), 2018
We review recent developments on the rôle of neutrino mixing in the inverse β decay of accelerate... more We review recent developments on the rôle of neutrino mixing in the inverse β decay of accelerated protons. We show that calculations in the inertial and comoving frames agree -thus preserving general covariance -only when taking neutrino asymptotic states to be flavor (rather than mass) eigenstates. Our conclusions are valid in the approximation in which Pontecorvo states are correctly representing neutrino flavor states. We speculate about the general case involving exact flavor states and finally comment on other approaches recently appeared in literature.
In this paper we study a unified formalism for Thermal Quantum Field Theories, i.e., for the Mats... more In this paper we study a unified formalism for Thermal Quantum Field Theories, i.e., for the Matsubara approach, Thermo Field Dynamics and the Path Ordered Method. To do so, we employ a mechanism akin to the Hawking effect which explores a relationship between the concept of temperature and spacetimes endowed with event-horizons. In particular, we consider an eight dimensional static spacetime, the so-called η-ξ spacetime, which we show to form an appropriate geometric background for generic Thermal Quantum Field Theories. Within this framework, the different formalisms of Thermal Field Theory are unified in a very natural way via various analytical continuations and the set of time-paths used in the Path Ordered Method is interpreted in geometric terms. We also explain reported inconsistencies inherent in the Thermo Field Dynamics through the appearance of horizons (and ensuing loss of information) in the η-ξ spacetime.
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the... more When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we propose a generalized generating functional for Green's functions which allows to easily distinguish among a continuous set of vacua that are mutually connected via unitary canonical transformations. In order to keep our discussion as simple as possible, we limit ourselves to Quantum Mechanics where the generating functional of Green's functions is constructed by means of phase-space path integrals. The quantum-mechanical setting allows to accentuate the main logical steps involved without embarking on technical complications such as renormalization or inequivalent representations that should otherwise be addressed in the full-fledged Quantum Field Theory. We illustrate the inner workings of the generating functional obtained by discussing Green's functions among vacua that are mutually connected via translations and dilatations. Salient issues, including connection with Quantum Field Theory, vacuum-to-vacuum transition amplitudes and perturbation expansion in the vacuum parameter are also briefly discussed.
Intrinsic quantum correlations supported by the SU (2) ⊗ SU (2) structure of the Dirac equation u... more Intrinsic quantum correlations supported by the SU (2) ⊗ SU (2) structure of the Dirac equation used to describe particle/antiparticle states, optical ion traps and bilayer graphene are investigated and connected to the description of local properties of Dirac bi-spinors. For quantum states driven by Dirac-like Hamiltonians, quantum entanglement and geometric discord between spin and parity degrees of freedom-sometimes mapped into equivalent low energy internal degrees of freedom-are obtained. Such spin-parity quantum correlations and the corresponding nonlocal intrinsic structures of bi-spinor fermionic states can be classified in order to relate quantum observables to the (non)local behavior of these correlations. It is shown that free particle mixed states do not violate the Clauser-Horne-Shymony-Holt inequality: the correlations in such mixed bi-spinors, although quantum, can be reproduced by a suitable local hidden variable model. Additionally, the effects due to a non-minimal coupling to a homogeneous magnetic field, and to the inclusion of thermal effects are evaluated, and quantum correlations of associated quantum mixtures and of the thermal states are all quantified.The above-mentioned correlation quantifiers are then used to measure the influence of CP transformations on spin-parity quantum correlations, and our results show that quantum entanglement is invariant under CP transformations, although the geometric discord is highly sensitive to the CP symmetry.
In line with a series of previous works, in this paper we discuss the inverse β-decay of accelera... more In line with a series of previous works, in this paper we discuss the inverse β-decay of accelerated protons p → n + e + + νe . To make the calculation of the transition rate easier to handle, we focus on an ideal “twin-process”, assuming the counterparts of lepton fields to be scalars. The rate of p → n conversions is evaluated in both the laboratory and comoving frames, showing that the two results perfectly agree due to the Unruh effect. In spite of the minimal setting, we stress that this model is an attempt to wash technical difficulties out of the analysis of the inverse β-decay. The future goal is to investigate the concerns recently raised in literature about the compatibility of the two rates when neutrino mixing is taken into account.
In this paper we study patterns of dynamical symmetry breaking for a class of models characterize... more In this paper we study patterns of dynamical symmetry breaking for a class of models characterized by SU (3)V × SU (3)A × U (1)V chiral-flavor symmetry. In particular, we show how dynamical mixing generation implies the existence of exotic condensates on vacuum, mixing fermion and antifermions with different flavors. By means of Ward-Takahashi identities we also derive Haag expansions for Nambu-Goldstone fields.
In the quantum field theory framework, both flavour mixing and Unruh effect have been shown to ar... more In the quantum field theory framework, both flavour mixing and Unruh effect have been shown to arise from Bogoliubov transformations connecting inequivalent Hilbert spaces. In the present work, we study how these transformations combine when field mixing for an accelerated observer (Rindler observer) is considered. In particular, a simplified two-flavour model involving Dirac neutrino fields is analyzed. In spite of such basic setting, we find that the spectrum of Unruh radiation gets significantly modified, losing its characteristic thermal behaviour. Exploiting this result, the possibility of fixing new constraints on the neutrino squared mass differences is investigated.
Mixing transformations for a uniformly accelerated observer (Rindler observer) are analyzed withi... more Mixing transformations for a uniformly accelerated observer (Rindler observer) are analyzed within the quantum field theory framework as a basis for investigating gravitational effects on flavor oscillations. In particular, the case of two charged boson fields with different masses is discussed. In spite of such a minimal setting, the standard Unruh radiation is found to loose its characteristic thermal interpretation due to the interplay between the Bogolubov transformation hiding in field mixing and the one arising from the Rindler spacetime structure. The modified spectrum detected by the Rindler observer is explicitly calculated in the limit of small mass difference.
The European Physical Journal Special Topics, 2017
We propose the use of specific dynamical processes and more in general of ideas from Physics to m... more We propose the use of specific dynamical processes and more in general of ideas from Physics to model the evolution in time of musical structures. We apply this approach to two Études by F. Chopin, namely op.10 n.3 and op.25 n.1, proposing some original description based on concepts of symmetry breaking/restoration and quantum coherence, which could be useful for interpretation. In this analysis, we take advantage of colored musical scores, obtained by implementing Scriabin's color code for sounds to musical notation.
An important feature of Quantum Field Theory is the existence of unitarily inequivalent represent... more An important feature of Quantum Field Theory is the existence of unitarily inequivalent representations of canonical commutation relations. When one works with the functional integral formalism, it is not clear, however, how this feature emerges. By following the seminal work of M. Swanson on canonical transformations in phase-space path integral, we generalize his approach to coherent-state functional integrals which in turn will lead to a simplified formalism which makes the appearance of the inequivalent representations more transparent. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
We study the mixing of two complex boson fields with different masses in Rindler spacetime. We fi... more We study the mixing of two complex boson fields with different masses in Rindler spacetime. We find that the Bogoliubov transformation associated with field mixing combines in a non-trivial way with the thermal Bogoliubov transformation associated to the uniformly accelerated observer (Rindler observer): as a result, the spectrum of Unruh radiation gets modified.
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact... more We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems and thermal field theories is discussed and the doubled variables are related to quantum noise effects. The 't Hooft proposal, according to which the loss of information due to dissipation in a classical deterministic system manifests itself in the quantum features of the system, is analyzed and the quantum spectrum of the harmonic oscillator is shown to be originated from the dissipative character of the original classical deterministic system.
We present the exact formula for neutrino oscillations. By resorting to recent results of Quantum... more We present the exact formula for neutrino oscillations. By resorting to recent results of Quantum Field Theory of fermion mixing, we work out the Green's function formalism for mixed neutrinos. This allows us to obtain an additional term with different oscillation frequency. The usual quantum mechanical Pontecorvo formula is recovered in the relativistic limit.
Journal of Physics A: Mathematical and General, 1999
We look at a real scalar field in thermal equilibrium in the context of the new normal ordering a... more We look at a real scalar field in thermal equilibrium in the context of the new normal ordering and field split defined by Evans and Steer [1]. We show that the field split defines a natural canonical transformation, but that this transformation differs from others known in thermal field theory.
The Green's function formalism for neutrino mixing is presented and the exact oscillation formula... more The Green's function formalism for neutrino mixing is presented and the exact oscillation formula is obtained. The usual Pontecorvo formula is recovered in the relativistic limit.
By resorting to recent results on fermion mixing which show that the Fock space of definite flavo... more By resorting to recent results on fermion mixing which show that the Fock space of definite flavor states is unitarily inequivalent to the Fock space of definite mass states, we discuss the phenomenological implications on the neutrino oscillation formula. For finite momentum the oscillation amplitude is depressed, or "squeezed", by a momentum dependent factor. In the relativistic limit the conventional oscillation formula is recovered.
We discuss some recent results on neutrino physics in the context of the inverse β-decay of unifo... more We discuss some recent results on neutrino physics in the context of the inverse β-decay of uniformly accelerated protons. Specifically, we compute the decay rate of the process p → n + e + + ν in both the laboratory frame (where the proton is non-inertial) and the comoving frame (where the proton is at rest and interacts with a thermal bath of electrons and neutrinos due to the Unruh effect). On the basis of the sole requirement of General Covariance of Quantum Field Theory, we manage to show that: i) the asymptotic (i.e. “in” and “out” ) neutrino states to be used for the evaluation of the S-matrix are Pontecorvo flavor eigenstates, ii) the Unruh thermal bath must be made up of oscillating neutrinos.
Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017), 2018
We review recent developments on the rôle of neutrino mixing in the inverse β decay of accelerate... more We review recent developments on the rôle of neutrino mixing in the inverse β decay of accelerated protons. We show that calculations in the inertial and comoving frames agree -thus preserving general covariance -only when taking neutrino asymptotic states to be flavor (rather than mass) eigenstates. Our conclusions are valid in the approximation in which Pontecorvo states are correctly representing neutrino flavor states. We speculate about the general case involving exact flavor states and finally comment on other approaches recently appeared in literature.
In this paper we study a unified formalism for Thermal Quantum Field Theories, i.e., for the Mats... more In this paper we study a unified formalism for Thermal Quantum Field Theories, i.e., for the Matsubara approach, Thermo Field Dynamics and the Path Ordered Method. To do so, we employ a mechanism akin to the Hawking effect which explores a relationship between the concept of temperature and spacetimes endowed with event-horizons. In particular, we consider an eight dimensional static spacetime, the so-called η-ξ spacetime, which we show to form an appropriate geometric background for generic Thermal Quantum Field Theories. Within this framework, the different formalisms of Thermal Field Theory are unified in a very natural way via various analytical continuations and the set of time-paths used in the Path Ordered Method is interpreted in geometric terms. We also explain reported inconsistencies inherent in the Thermo Field Dynamics through the appearance of horizons (and ensuing loss of information) in the η-ξ spacetime.
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the... more When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we propose a generalized generating functional for Green's functions which allows to easily distinguish among a continuous set of vacua that are mutually connected via unitary canonical transformations. In order to keep our discussion as simple as possible, we limit ourselves to Quantum Mechanics where the generating functional of Green's functions is constructed by means of phase-space path integrals. The quantum-mechanical setting allows to accentuate the main logical steps involved without embarking on technical complications such as renormalization or inequivalent representations that should otherwise be addressed in the full-fledged Quantum Field Theory. We illustrate the inner workings of the generating functional obtained by discussing Green's functions among vacua that are mutually connected via translations and dilatations. Salient issues, including connection with Quantum Field Theory, vacuum-to-vacuum transition amplitudes and perturbation expansion in the vacuum parameter are also briefly discussed.
Intrinsic quantum correlations supported by the SU (2) ⊗ SU (2) structure of the Dirac equation u... more Intrinsic quantum correlations supported by the SU (2) ⊗ SU (2) structure of the Dirac equation used to describe particle/antiparticle states, optical ion traps and bilayer graphene are investigated and connected to the description of local properties of Dirac bi-spinors. For quantum states driven by Dirac-like Hamiltonians, quantum entanglement and geometric discord between spin and parity degrees of freedom-sometimes mapped into equivalent low energy internal degrees of freedom-are obtained. Such spin-parity quantum correlations and the corresponding nonlocal intrinsic structures of bi-spinor fermionic states can be classified in order to relate quantum observables to the (non)local behavior of these correlations. It is shown that free particle mixed states do not violate the Clauser-Horne-Shymony-Holt inequality: the correlations in such mixed bi-spinors, although quantum, can be reproduced by a suitable local hidden variable model. Additionally, the effects due to a non-minimal coupling to a homogeneous magnetic field, and to the inclusion of thermal effects are evaluated, and quantum correlations of associated quantum mixtures and of the thermal states are all quantified.The above-mentioned correlation quantifiers are then used to measure the influence of CP transformations on spin-parity quantum correlations, and our results show that quantum entanglement is invariant under CP transformations, although the geometric discord is highly sensitive to the CP symmetry.
In line with a series of previous works, in this paper we discuss the inverse β-decay of accelera... more In line with a series of previous works, in this paper we discuss the inverse β-decay of accelerated protons p → n + e + + νe . To make the calculation of the transition rate easier to handle, we focus on an ideal “twin-process”, assuming the counterparts of lepton fields to be scalars. The rate of p → n conversions is evaluated in both the laboratory and comoving frames, showing that the two results perfectly agree due to the Unruh effect. In spite of the minimal setting, we stress that this model is an attempt to wash technical difficulties out of the analysis of the inverse β-decay. The future goal is to investigate the concerns recently raised in literature about the compatibility of the two rates when neutrino mixing is taken into account.
In this paper we study patterns of dynamical symmetry breaking for a class of models characterize... more In this paper we study patterns of dynamical symmetry breaking for a class of models characterized by SU (3)V × SU (3)A × U (1)V chiral-flavor symmetry. In particular, we show how dynamical mixing generation implies the existence of exotic condensates on vacuum, mixing fermion and antifermions with different flavors. By means of Ward-Takahashi identities we also derive Haag expansions for Nambu-Goldstone fields.
In the quantum field theory framework, both flavour mixing and Unruh effect have been shown to ar... more In the quantum field theory framework, both flavour mixing and Unruh effect have been shown to arise from Bogoliubov transformations connecting inequivalent Hilbert spaces. In the present work, we study how these transformations combine when field mixing for an accelerated observer (Rindler observer) is considered. In particular, a simplified two-flavour model involving Dirac neutrino fields is analyzed. In spite of such basic setting, we find that the spectrum of Unruh radiation gets significantly modified, losing its characteristic thermal behaviour. Exploiting this result, the possibility of fixing new constraints on the neutrino squared mass differences is investigated.
Mixing transformations for a uniformly accelerated observer (Rindler observer) are analyzed withi... more Mixing transformations for a uniformly accelerated observer (Rindler observer) are analyzed within the quantum field theory framework as a basis for investigating gravitational effects on flavor oscillations. In particular, the case of two charged boson fields with different masses is discussed. In spite of such a minimal setting, the standard Unruh radiation is found to loose its characteristic thermal interpretation due to the interplay between the Bogolubov transformation hiding in field mixing and the one arising from the Rindler spacetime structure. The modified spectrum detected by the Rindler observer is explicitly calculated in the limit of small mass difference.
The European Physical Journal Special Topics, 2017
We propose the use of specific dynamical processes and more in general of ideas from Physics to m... more We propose the use of specific dynamical processes and more in general of ideas from Physics to model the evolution in time of musical structures. We apply this approach to two Études by F. Chopin, namely op.10 n.3 and op.25 n.1, proposing some original description based on concepts of symmetry breaking/restoration and quantum coherence, which could be useful for interpretation. In this analysis, we take advantage of colored musical scores, obtained by implementing Scriabin's color code for sounds to musical notation.
An important feature of Quantum Field Theory is the existence of unitarily inequivalent represent... more An important feature of Quantum Field Theory is the existence of unitarily inequivalent representations of canonical commutation relations. When one works with the functional integral formalism, it is not clear, however, how this feature emerges. By following the seminal work of M. Swanson on canonical transformations in phase-space path integral, we generalize his approach to coherent-state functional integrals which in turn will lead to a simplified formalism which makes the appearance of the inequivalent representations more transparent. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
We study the mixing of two complex boson fields with different masses in Rindler spacetime. We fi... more We study the mixing of two complex boson fields with different masses in Rindler spacetime. We find that the Bogoliubov transformation associated with field mixing combines in a non-trivial way with the thermal Bogoliubov transformation associated to the uniformly accelerated observer (Rindler observer): as a result, the spectrum of Unruh radiation gets modified.
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact... more We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems and thermal field theories is discussed and the doubled variables are related to quantum noise effects. The 't Hooft proposal, according to which the loss of information due to dissipation in a classical deterministic system manifests itself in the quantum features of the system, is analyzed and the quantum spectrum of the harmonic oscillator is shown to be originated from the dissipative character of the original classical deterministic system.
We present the exact formula for neutrino oscillations. By resorting to recent results of Quantum... more We present the exact formula for neutrino oscillations. By resorting to recent results of Quantum Field Theory of fermion mixing, we work out the Green's function formalism for mixed neutrinos. This allows us to obtain an additional term with different oscillation frequency. The usual quantum mechanical Pontecorvo formula is recovered in the relativistic limit.
Journal of Physics A: Mathematical and General, 1999
We look at a real scalar field in thermal equilibrium in the context of the new normal ordering a... more We look at a real scalar field in thermal equilibrium in the context of the new normal ordering and field split defined by Evans and Steer [1]. We show that the field split defines a natural canonical transformation, but that this transformation differs from others known in thermal field theory.
The Green's function formalism for neutrino mixing is presented and the exact oscillation formula... more The Green's function formalism for neutrino mixing is presented and the exact oscillation formula is obtained. The usual Pontecorvo formula is recovered in the relativistic limit.
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Papers by M. Blasone