The role of the environment initial conditions in the breaking of the time reversal symmetry of e... more The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ǫ-prescription where the non-uniform convergence of the limit ǫ → 0 leaves behind a spontaneous breakdown of the time reversal symmetry. Contents I. Introduction II. Classical effective theories III. A single degree of freedom A. Classical chronon-dynamics B. Harmonic systems C. Generalized ǫ-prescription D. Mechanical time arrow IV. Open systems in the thermodynamical limit A. Effective chronon theory B. Energy balance C. Normal modes I.: Finite system D. Normal modes II.: Infinite system E. Toy model V. Finite life-time and decoherence A. Quantum chronon-dynamics
The master equation for the reduced density matrix of a charged particle interacting with a trans... more The master equation for the reduced density matrix of a charged particle interacting with a translation invariant weakly coupled environment is considered. The electric current is renormalized by the system-environment interaction, leading to a direct signature of the environment in the bremsstrahlung. The general solution is given in the absence of the external electromagnetic field and the spread and the decoherence of a wave packet are followed. The increased complexity and importance of the boundary conditions for the density matrix are pointed out.
The role of the environment initial conditions in the breaking of the time reversal symmetry of e... more The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized-prescription where the non-uniform convergence of the limit → 0 leaves behind a spontaneous breakdown of the time reversal symmetry.
Some features of the high temperature gluonic matter, such as the breakdown of the fundamental gr... more Some features of the high temperature gluonic matter, such as the breakdown of the fundamental group symmetry by the kinetic energy, the screening of test quarks by some unusual gluon states and the explanation of the absence of isolated quarks in the vacuum without the help of infinities are presented in this talk. Special attention is paid to separate the dynamical input inferred from the numerical results of lattice gauge theory from the kinematics.
We discuss the problem of the quantization and dynamic evolution of a scalar free field in the in... more We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.
The blocking step of the renormalization group method is usually carried out by restricting it to... more The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ϕ 6 model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.
A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to ... more A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to remarkable energetic features, arising from the competition of different saddle points in the partition function. We describe this competition for finite temperature at equilibrium, taking into account both static and (Euclidean) time-dependent saddle points. The effective theory for the homogeneous order parameter yields a non-extensive vacuum energy at low temperatures, implying a dynamical violation of the Null Energy Condition.
The decoherence of a test particle interacting with an ideal gas is studied by the help of the ef... more The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order O ∂ 2 t. The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.
Renormalization group in the internal space consists of the gradual change of the coupling consta... more Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.
We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is n... more We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is non perturbative and contains a condensate of the metric tensor in a manner reminiscent of Yang-Mills theories. As a simple step toward the characterization of such a vacuum the value of the one-loop effective action is computed for Euclidean de Sitter spaces as a function of the curvature when the unstable conformal modes are held fixed. Two phases are found, one where the curvature is large and gravitons should be confined and another one which appears to be weakly coupled and tends to be flat. The induced cosmological constant is positive or negative in the strongly or weakly curved phase, respectively. The relevance of the Casimir effect in understanding the UV sensitivity of gravity is pointed out.
HAL (Le Centre pour la Communication Scientifique Directe), 2005
Renormalization group in the internal space consists of the gradual change of the coupling consta... more Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.
The particle and current densities are shown to display damping and undergo decoherence in ideal ... more The particle and current densities are shown to display damping and undergo decoherence in ideal quantum gases. The damping is read off from the equations of motion reminiscent of the Navier-Stokes equations and shows some formal similarity with Landau damping. The decoherence leads to consistent density and current histories with characteristic length and time scales given by the ideal gas.
Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The form... more Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial state. These types of decoherence are computed in the case of the Brownian motion and the harmonic and anharmonic oscillators within the semiclassical approximation. A remarkable phenomenon, namely the opposite orientation of the time arrow of the dynamical variables compared to that of the quantum fluctuations generates a double exponential time dependence of the dynamical decoherence in the presence of a harmonic force. For the weakly anharmonic oscillator the dynamical decoherence is found to depend in a singular way on the amount of the anharmonicity.
The effective Lagrangian of a test particle, interacting within an ideal gas, is calculated withi... more The effective Lagrangian of a test particle, interacting within an ideal gas, is calculated within the closed time path formalism in the one-loop approximation and in the leading order of the particle trajectory. The expansion in the time derivative, available for slow enough motion, uncovers diffusive forces and decoherence in the particle coordinate basis. The master equation, generated by the effective Lagrangian, is derived and its consistency is verified for a finite-temperature gas.
A c-number path integral representation is constructed for the solution of the Dirac equation. Th... more A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the spin and the chirality flips.
The role of the environment initial conditions in the breaking of the time reversal symmetry of e... more The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ǫ-prescription where the non-uniform convergence of the limit ǫ → 0 leaves behind a spontaneous breakdown of the time reversal symmetry. Contents I. Introduction II. Classical effective theories III. A single degree of freedom A. Classical chronon-dynamics B. Harmonic systems C. Generalized ǫ-prescription D. Mechanical time arrow IV. Open systems in the thermodynamical limit A. Effective chronon theory B. Energy balance C. Normal modes I.: Finite system D. Normal modes II.: Infinite system E. Toy model V. Finite life-time and decoherence A. Quantum chronon-dynamics
The master equation for the reduced density matrix of a charged particle interacting with a trans... more The master equation for the reduced density matrix of a charged particle interacting with a translation invariant weakly coupled environment is considered. The electric current is renormalized by the system-environment interaction, leading to a direct signature of the environment in the bremsstrahlung. The general solution is given in the absence of the external electromagnetic field and the spread and the decoherence of a wave packet are followed. The increased complexity and importance of the boundary conditions for the density matrix are pointed out.
The role of the environment initial conditions in the breaking of the time reversal symmetry of e... more The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized-prescription where the non-uniform convergence of the limit → 0 leaves behind a spontaneous breakdown of the time reversal symmetry.
Some features of the high temperature gluonic matter, such as the breakdown of the fundamental gr... more Some features of the high temperature gluonic matter, such as the breakdown of the fundamental group symmetry by the kinetic energy, the screening of test quarks by some unusual gluon states and the explanation of the absence of isolated quarks in the vacuum without the help of infinities are presented in this talk. Special attention is paid to separate the dynamical input inferred from the numerical results of lattice gauge theory from the kinematics.
We discuss the problem of the quantization and dynamic evolution of a scalar free field in the in... more We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.
The blocking step of the renormalization group method is usually carried out by restricting it to... more The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ϕ 6 model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.
A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to ... more A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to remarkable energetic features, arising from the competition of different saddle points in the partition function. We describe this competition for finite temperature at equilibrium, taking into account both static and (Euclidean) time-dependent saddle points. The effective theory for the homogeneous order parameter yields a non-extensive vacuum energy at low temperatures, implying a dynamical violation of the Null Energy Condition.
The decoherence of a test particle interacting with an ideal gas is studied by the help of the ef... more The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order O ∂ 2 t. The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.
Renormalization group in the internal space consists of the gradual change of the coupling consta... more Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.
We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is n... more We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is non perturbative and contains a condensate of the metric tensor in a manner reminiscent of Yang-Mills theories. As a simple step toward the characterization of such a vacuum the value of the one-loop effective action is computed for Euclidean de Sitter spaces as a function of the curvature when the unstable conformal modes are held fixed. Two phases are found, one where the curvature is large and gravitons should be confined and another one which appears to be weakly coupled and tends to be flat. The induced cosmological constant is positive or negative in the strongly or weakly curved phase, respectively. The relevance of the Casimir effect in understanding the UV sensitivity of gravity is pointed out.
HAL (Le Centre pour la Communication Scientifique Directe), 2005
Renormalization group in the internal space consists of the gradual change of the coupling consta... more Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.
The particle and current densities are shown to display damping and undergo decoherence in ideal ... more The particle and current densities are shown to display damping and undergo decoherence in ideal quantum gases. The damping is read off from the equations of motion reminiscent of the Navier-Stokes equations and shows some formal similarity with Landau damping. The decoherence leads to consistent density and current histories with characteristic length and time scales given by the ideal gas.
Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The form... more Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial state. These types of decoherence are computed in the case of the Brownian motion and the harmonic and anharmonic oscillators within the semiclassical approximation. A remarkable phenomenon, namely the opposite orientation of the time arrow of the dynamical variables compared to that of the quantum fluctuations generates a double exponential time dependence of the dynamical decoherence in the presence of a harmonic force. For the weakly anharmonic oscillator the dynamical decoherence is found to depend in a singular way on the amount of the anharmonicity.
The effective Lagrangian of a test particle, interacting within an ideal gas, is calculated withi... more The effective Lagrangian of a test particle, interacting within an ideal gas, is calculated within the closed time path formalism in the one-loop approximation and in the leading order of the particle trajectory. The expansion in the time derivative, available for slow enough motion, uncovers diffusive forces and decoherence in the particle coordinate basis. The master equation, generated by the effective Lagrangian, is derived and its consistency is verified for a finite-temperature gas.
A c-number path integral representation is constructed for the solution of the Dirac equation. Th... more A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the spin and the chirality flips.
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Papers by Janos Polonyi