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P. Jizba

Publications and source records attributed to P. Jizba.

13 recordsLinked to original sources
arXiv2018

On the canonical quantization of the electromagnetic field and the emergence of gauge invariance

In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered for the longitudinal and the scalar photon fields. As a result we obtain that the relation holds which in the traditional approach is called the Gupta-Bleuler condition. Gauge invariance emerges as a property of the physical states. The group structure of the theory is recognized to be the one of $SU(2) \otimes SU(1,1)$.

quant-ph↗
arXiv2014

A framework for dynamical generation of flavor mixing

We present a dynamical mechanism à la Nambu--Jona-Lasinio for the generation of masses and mixing for two interacting fermion fields. The analysis is carried out in the framework introduced long ago by Umezawa et al., in which mass generation is achieved via inequivalent representations, and that we generalize to the case of two generations. The method allows a clear identification of the vacuum structure for each physical phase, confirming previous results about the distinct physical nature of the vacuum for fields with definite mass and fields with definite flavor. Implications for the leptonic sector of the Standard Model are briefly discussed.

hep-ph↗
arXiv2009

Dissipation and quantization for composite systems

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.

quant-ph↗
arXiv2005

Quantum Behavior of Deterministic Systems with Information Loss. Path Integral Approach

't Hooft's derivation of quantum from classical physics is analyzed by means of the classical path integral of Gozzi et al.. It is shown how the key element of this procedure - the loss of information constraint - can be implemented by means of Faddeev-Jackiw's treatment of constrained systems. It is argued that the emergent quantum systems are identical with systems obtained in [Phys.Rev. A 71 (2005) 052507] through Dirac-Bergmann's analysis. We illustrate our approach with two simple examples - free particle and linear harmonic oscillator. Potential Liouville anomalies are shown to be absent.

quant-ph↗
arXiv2004

Quantum fields with topological defects

Domain walls, strings and monopoles are extended objects, or defects, of quantum origin with topologically non--trivial properties and macroscopic behavior. They are described in Quantum Field Theory in terms of inhomogeneous condensates. We review the related formalism in the framework of the spontaneous breakdown of symmetry.

math-ph↗
arXiv2003

Hydrostatic Pressure of the O(N) $ϕ^4$ Theory in the Large N Limit

With non-equilibrium applications in mind we present in this paper a self-contained calculation of the hydrostatic pressure of the O(N)λϕ^4 theory at finite temperature. By combining the Keldysh-Schwinger closed-time path formalism with thermal Dyson-Schwinger equations we compute in the large N limit the hydrostatic pressure in a fully resumed form. We also calculate the high-temperature expansion for the pressure (in D=4) using the Mellin transform technique. The result obtained extends the results found by Drummond et al. [hep-ph/9708426] and Amelino-Camelia and Pi [hep-ph/9211211]. The latter are reproduced in the limits m_r(0)\to 0, T \to \infty and T \to \infty, respectively. Important issues of renormalizibility of composite operators at finite temperature are addressed and the improved energy-momentum tensor is constructed. The utility of the hydrostatic pressure in the non-equilibrium quantum systems is discussed.

hep-th↗
arXiv2003

Quantum limit of deterministic theories

We show that the quantum linear harmonic oscillator can be obtained in the large $N$ limit of a classical deterministic system with SU(1,1) dynamical symmetry. This is done in analogy with recent work by G.'t Hooft who investigated a deterministic system based on SU(2). Among the advantages of our model based on a non--compact group is the fact that the ground state energy is uniquely fixed by the choice of the representation.

quant-ph↗
arXiv2003

Dissipation, Emergent Quantization and Quantum Fluctuations

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.

quant-ph↗
arXiv2002

Quantization, group contraction and zero point energy

We study algebraic structures underlying 't Hooft's construction relating classical systems with the quantum harmonic oscillator. The role of group contraction is discussed. We propose the use of SU(1,1) for two reasons: because of the isomorphism between its representation Hilbert space and that of the harmonic oscillator and because zero point energy is implied by the representation structure. Finally, we also comment on the relation between dissipation and quantization.

quant-ph↗
arXiv2000

One particular approach to the non-equilibrium quantum dynamics

We present a particular approach to the non-equilibrium dynamics of quantum field theory. This approach is based on the Jaynes-Gibbs principle of the maximal entropy and its implementation, throghout the initial value data, into the dynamical equations for Green's functions.

hep-th↗
arXiv1998

Pressure of the Non-equilibrium O(N) Phi^{4} Theory in the Large N Limit

We calculate the off-equilibrium hydrostatic pressure for the O(N) Phi^{4} theory to the leading order in 1/N. The present paper, the first of a series, concentrates on the calculation of pressure in the non-equilibrium but translationally invariant medium. The Jaynes-Gibbs principle of maximal entropy is used to introduce the relevant density matrix which is then directly implemented into dynamical equations through generalised Kubo-Martin-Schwinger (KMS) conditions. We show that in the large N limit use of Ward identities enables the pressure to be expressed in terms of two point Green's functions. These satisfy the Kadanoff-Baym equations which are exactly solvable, and we explicitly calculate the pressure for three illustrative choices of ρ.

hep-th↗
arXiv1998

The Jaynes-Gibbs principle of maximal entropy and the non-equilibrium propagators of the O(N) phi^4 theory at large N

We present a novel procedure for calculating non-equilibrium two-point Green's functions in the $O(N) ϕ^{4}$ theory at large $N$. The non-equilibrium density matrix $ρ$ is constructed via the Jaynes-Gibbs principle of maximal entropy and it is directly implemented into the Dyson-Schwinger equations through initial value conditions. In the large $N$ limit we perform an explicit evaluation of two-point Green's functions for two illustrative choices of $ρ$.

hep-th↗