Papers by Horacio Girotti
Lettere al Nuovo Cimento, 1971
Classical and Quantum Dynamics of Constrained Systems
University of Heidelberg preprint
Nuclear Physics B, 1974
It is found that the extension of a local theory of fields, specifically quantum electrodynamics,... more It is found that the extension of a local theory of fields, specifically quantum electrodynamics, to a space of continuous dimensionality together with a systematic interpretation of the relativistically invariant functions as distributions, gives rise to a rather formal but operative machinery which naturally leads to the existence of non-vanishing c-number Schwinger and seagull terms. In fact, with this kind of tool at hand, no ad hoc definitions are required to deal with products of field operators taken at the same space-time point. We present a complete analysis of the behavior of Schwinger and seagull terms as analytic functions of the number of dimensions of the space (v). It is also shown that the Feynman conjecture (cancellation of Schwinger terms with divergences of seagulls) holds for arbitrary v.
Physics Letters B, 1992
The effective nonrelativistic potential VT describing the fermion-fermion interaction in the Maxw... more The effective nonrelativistic potential VT describing the fermion-fermion interaction in the Maxwell-Chern-Simons theory is derived to the lowest order in perturbation theory. As expected, VT is not invariant under parity and time-reversal transformations. The quantum dynamics generated by Vr becomes exactly solvable at the limits where either the Maxwell or the Chern-Simons terms disappear; in neither case electron-electron bound states show up. However, numerical calculations indicate that fermion-fermion bound states do exist in the general case.
Physics Letters A, 1994
The operator and the functional formulations of the dynamics of constrained systems are explored ... more The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
Physical Review D, 2006
In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formu... more In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formulated in a noncommutative space-time. We show that, unlike in some recent analysis of quantum gravity effects, supersymmetry does not protect the theory from the large Lorentz violating effects arising from the loop corrections. We take advantage of the noncommutative Wess-Zumino model to illustrate this point.
eprint arXiv: hep-th/0211176
This paper is dedicated to the study of the existence and the properties of electronelectron boun... more This paper is dedicated to the study of the existence and the properties of electronelectron bound states in QED 3. A detailed analysis of the infrared structure of the perturbative series of the theory is presented. We start by analyzing the two-point Green's function, in the Bloch-Nordsieck approximation. The theory appears to be plagued by severe infrared divergencies, which nevertheless disappear when vacuumpolarization effects are non-perturbatively taken into account. The dynamical induction of a Chern-Simons term is at the root of this mechanism. From the inspection of the electron-electron non-relativistic potential it then follows that equally charged fermions may either repel or attract and, moreover, that bound states do in fact exist in the theory. We calculate numerically the binding energies and average radius of the bound states. We find an accidental quasi-degeneracy of the ground state of the system, between the lowest-energy l = −3 and l = −5 states, which could be related to a radio-frequency resonance in high-T c superconductors.
Nuclear Physics B, 2000
We show that the noncommutative Wess-Zumino model is renormalizable to all orders of perturbation... more We show that the noncommutative Wess-Zumino model is renormalizable to all orders of perturbation theory. The noncommutative scalar potential by itself is non-renormalizable but the Yukawa terms demanded by supersymmetry improve the situation turning the theory into a renormalizable one. As in the commutative case, there are neither quadratic nor linear divergences. Hence, the IR/UV mixing does not give rise to quadratic infrared poles.
We study in detail the quantization of a model which apparently describes chiral bosons. The mode... more We study in detail the quantization of a model which apparently describes chiral bosons. The model is based on the idea that the chiral condition could be implemented through a linear constraint. We show that the space of states is of indefinite metric. We cure this disease by introducing ghost fields in such a way that a BRST symmetry is generated. A quartet algebra is seen to emerge. The quartet mechanism, then, forces all physical states, but the vacuum, to have zero norm.
We study the one-loop quantum corrections to the U(N) noncommutative supersymmetric Yang-Mills th... more We study the one-loop quantum corrections to the U(N) noncommutative supersymmetric Yang-Mills theory in three spacetime dimensions (NCSYM_3). We show that the cancellation of the dangerous UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. Furthermore, in the one-loop approximation, the would be subleading UV and UV/IR infrared divergences are shown to vanish.
Commutative four dimensional supersymmetric Yang-Mills (SYM) is known to be renormalizable for N ... more Commutative four dimensional supersymmetric Yang-Mills (SYM) is known to be renormalizable for N = 1, 2, and finite for N = 4. However, in the noncommutative version of the model the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of the N = 1, 2, 4 noncommutative supersymmetric Yang-Mills theory with gauge group U(N) (NCSYM). We employ the covariant superfield framework to compute the one-loop corrections to the two- and three-point functions of the gauge superfield V. It is found that the cancellation of the harmful UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. We argue that this is in agreement with the low energy limit of the open superstring in the presence of an external magnetic field. As expected, the planar sector of the two-point function of the V superfield exhibits UV divergences. They are found to cancel, in the Feynman g...
Vacuum polarization effects are non-perturbatively incorporated into the photon propagator to eli... more Vacuum polarization effects are non-perturbatively incorporated into the photon propagator to eliminate the severe infrared problems characteristic of QED3. The theory is thus rephrased in terms of a massive vector boson whose mass is e 2 /(8π). Subsequently, it is shown that electron-electron bound states are possible in QED3. PACS: 11.10.St, 11.15.Tk Typeset Using REVTEXRecently [1], the effective non-relativistic potential
Commutative four dimensional supersymmetric Yang-Mills (SYM) is known to be renormalizable for N ... more Commutative four dimensional supersymmetric Yang-Mills (SYM) is known to be renormalizable for N = 1, 2, and finite for N = 4. However, in the noncommutative version of the model the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of the N = 1, 2, 4 noncommutative supersymmetric Yang-Mills theory with gauge group U(N) (NCSYM). We employ the covariant superfield framework to compute the one-loop corrections to the two- and three-point functions of the gauge superfield V. It is found that the cancellation of the harmful UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. We argue that this is in agreement with the low energy limit of the open superstring in the presence of an external magnetic field. As expected, the planar sector of the two-point function of the V superfield exhibits UV divergences. They are found to cancel, in the Feynman g...
We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system... more We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the appearance of the UV/IR mechanism is exemplified. The emphasis is on finding and analyzing noncommutative quantum field theories which are renormalizable and free of nonintegrable infrared singularities. In this last connection we give a detailed discussion of the quantization of the noncommutative Wess-Zumino model as well as of its low energy behavior. Lectures delivered at the XII Sumer School Jorge Andre Swieca. Section Particles and Fields,
Vacuum polarization effects are non-perturbatively incorporated into the photon propagator to eli... more Vacuum polarization effects are non-perturbatively incorporated into the photon propagator to eliminate the severe infrared problems characteristic of QED3. The theory is thus rephrased in terms of a massive vector boson whose mass is e 2 /(8π). Subsequently, it is shown that electron-electron bound states are possible in QED3. PACS: 11.10.St, 11.15.Tk Typeset Using REVTEXRecently [1], the effective non-relativistic potential
LETTER TO THE EDITOR The noncommutative degenerate electron gas
Abstract. The quantum dynamics of nonrelativistic single particle systems involving noncommutativ... more Abstract. The quantum dynamics of nonrelativistic single particle systems involving noncommutative coordinates, usually referred to as noncommutative quantum mechanics, has lately been the object of several investigations. In this note we pursue these studies for the case of multi-particle systems. We use as a prototype the degenerate electron gas whose dynamics is well known in the commutative limit. Our central aim here is to understand qualitatively, rather than quantitatively, the main modifications induced by the presence of noncommutative coordinates. We shall first see that the noncommutativity modifies the exchange correlation energy while preserving the electric neutrality of the model. By employing time-independent perturbation theory together with the Seiberg-Witten map we show, afterwards, that the ionization potential is modified by the noncommutativity. It also turns out that the noncommutative parameter acts as a reference temperature. Hence, the noncommutativity lift...
We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system... more We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the appearance of the UV/IR mechanism is exemplified. The emphasis is on finding and analyzing noncommutative quantum field theories which are renormalizable and free of nonintegrable infrared singularities. In this last connection we give a detailed discussion of the quantization of the noncommutative Wess-Zumino model as well as of its low energy behavior. Lectures delivered at the XII Sumer School Jorge Andre Swieca. Section Particles and Fields,
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Papers by Horacio Girotti