Papers by Roberto De Pietri
Physical Review D, 2007
We study the high density region of QCD within an effective model obtained in the frame of the ho... more We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first idea of the phase structure, the model is analyzed in strong coupling expansion and using a mean field approximation. In numerical simulations, the model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density. We obtain in this way information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints for the behaviour of non-zero density QCD.
Physical Review D, 2007
We study the high density region of QCD within an effective model obtained in the frame of the ho... more We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first idea of the phase structure, the model is analyzed in strong coupling expansion and using a mean field approximation. In numerical simulations, the model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density. We obtain in this way information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints for the behaviour of non-zero density QCD.
We study the high density region of QCD within an effective model obtained in the frame of the ho... more We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov-type loops as the main dynamical variables representing the fermionic matter. This model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the simulated Monte Carlo ensemble with the true one. We review the main features of the model and present results concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the Polykov loop susceptibility, which may be used to characterize the various phases expected at high baryonic density. In this way, we obtain information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints about the behaviour of non-zero density QCD.
We study the high density region of QCD within an effective model obtained in the frame of the ho... more We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion. The model still acknowledges the sign problem peculiar to nonzero chemical potential, but it permits the development of refined algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model, including the most explicit form of the resumed expansion, and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density.
The problem of constructing a quantum theory of gravity has been tackled with very different stra... more The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which relying on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central rôle is played by combinatorial topology, often used to recover the space-time manifold from the other structures involved. An extremely attractive possibility is that of encoding all possible space-times as specific Feynman diagrams of a suitable field theory. In this work we analyze how exactly one can associate combinatorial 4-manifolds to the Feynman diagrams of certain tensor theories. PACS: 04.60.Nc, 02.40.Sf MSC (2000): 57Q05 (primary), 57M99 (secondary).
The problem of constructing a quantum theory of gravity has been tackled with very different stra... more The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which relying on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central rôle is played by combinatorial topology, often used to recover the space-time manifold from the other structures involved. An extremely attractive possibility is that of encoding all possible space-times as specific Feynman diagrams of a suitable field theory. In this work we analyze how exactly one can associate combinatorial 4-manifolds to the Feynman diagrams of certain tensor theories. PACS: 04.60.Nc, 02.40.Sf MSC (2000): 57Q05 (primary), 57M99 (secondary).
Classical and Quantum Gravity, 1997
Using Penrose's binor calculus for SU (2) (SL(2, C)) tensor expressions, a graphical method for t... more Using Penrose's binor calculus for SU (2) (SL(2, C)) tensor expressions, a graphical method for the connection representation of Euclidean Quantum Gravity (real connection) is constructed. It is explicitly shown that: (i) the recently proposed scalar product in the loop-representation coincide with the Ashtekar-Lewandowski cylindrical measure in the space of connections; (ii) it is possible to establish a correspondence between the operators in the connection representation and those in the loop representation. The construction is based on embedded spin network, the Penrose's graphical method of SU (2) calculus, and the existence of a generalized measure on the space of connections modulo gauge transformations. PACS numbers: 04.60.-m, 02.70.-c, 04.60.Ds, 03.70+k. Short title: On the relation between the connection and the loop representation February 7, 2008 † the term cylindrical function comes from the language of Wiener integration on an infinitedimensional space.
The canonical "loop" formulation of quantum gravity is a mathematically well defined, background ... more The canonical "loop" formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the theory are: 1) the complete calculation of the spectrum of geometric quantities like the area and the volume and the consequent physical predictions about the structure of the space-time at the Planck scale; 2) a microscopical derivation of the Bekenstein-Hawking black-hole entropy formula. Unfortunately, despite recent results, the dynamical aspect of the theory (imposition of the Wheller-De Witt constraint) remains elusive.
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Papers by Roberto De Pietri