RENORMALIZATION AND BOLTZMANN EQUATIONS IN THERMAL QUANTUM FIELD THEORY

1995 ◽  
Vol 10 (11) ◽  
pp. 1693-1700 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Boltzmann Equation ◽  
Renormalization Scheme ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Boltzmann Equations ◽  
Self Energy ◽  
Spatially Inhomogeneous ◽  
Thermo Field Dynamics ◽  
Self Consistent ◽  
Consistent Manner

The renormalization scheme in nonequilibrium thermal quantum field theories is reexamined. Instead of the self-energy diagonalization scheme, we propose to diagonalize Green’s function at equal time. This eliminates the problem of on-shell definition related to time-dependent energies and spatially inhomogeneous situations, and yields a Boltzmann equation that contains memory effect. The new diagonalization scheme and the derivation of the Boltzmann equation from it can be applied to any thermal situation. It allows the treatment of a nonequilibrium problem beyond perturbational calculations in a self-consistent manner. The results are applicable to both thermo field dynamics and the closed time path formalism.

THERMO FIELD DYNAMICS IN TIME REPRESENTATION

1994 ◽  
Vol 09 (07) ◽  
pp. 1153-1180 ◽  
Author(s):  
Y. YAMANAKA ◽  
H. UMEZAWA ◽  
K. NAKAMURA ◽  
T. ARIMITSU
Keyword(s):  
Kinetic Equation ◽  
Time Dependent ◽  
Nonequilibrium Systems ◽  
Renormalization Condition ◽  
Usual Definition ◽  
Time Representation ◽  
Self Energy ◽  
Thermo Field Dynamics ◽  
Self Consistent ◽  
Definition Of

Making use of the thermo field dynamics (TFD) we formulate a calculable method for time-dependent nonequilibrium systems in a time representation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the form of B−1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). The number parameter in B here is the observed number (the Heisenberg number) with a fluctuation. With the usual definition of the on-shell self-energy a self-consistent renormalization condition leads to a kinetic equation for the number parameter. This equation turns out to be the Boltzmann equation, from which the entropy law follows.

scholarly journals NONEQUILIBRIUM THERMO FIELD DYNAMICS FOR RELATIVISTIC COMPLEX SCALAR AND DIRAC FIELDS

2012 ◽  
Vol 27 (14) ◽  
pp. 1250078 ◽  
Author(s):  
YUICHI MIZUTANI ◽  
TOMOHIRO INAGAKI
Keyword(s):  
Chemical Potential ◽  
Relativistic Quantum ◽  
The Self ◽  
Quantum Field Theories ◽  
Renormalization Condition ◽  
Complex Scalar ◽  
Dirac Fields ◽  
Self Energy ◽  
Thermo Field Dynamics ◽  
Self Consistency

Relativistic quantum field theories for complex scalar and Dirac fields are investigated in nonequilibrium thermo field dynamics. The thermal vacuum is defined by the Bogoliubov transformed creation and annihilation operators. Two independent Bogoliubov parameters are introduced for a charged field. Its difference naturally induces the chemical potential. Time-dependent thermal Bogoliubov transformation generates the thermal counterterms. We fix the terms by the self-consistency renormalization condition. Evaluating the thermal self-energy under the self-consistency renormalization condition, we derive the quantum Boltzmann equations for the relativistic fields.

scholarly journals TWISTED QUANTUM FIELDS ON MOYAL AND WICK–VOROS PLANES ARE INEQUIVALENT

2009 ◽  
Vol 24 (22) ◽  
pp. 1721-1730 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
M. MARTONE
Keyword(s):  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Poincaré Group ◽  
Energy Diagram ◽  
Poincare Group ◽  
Self Energy ◽  
Moyal Plane ◽  
Noncommutative Parameter

The Moyal and Wick–Voros planes [Formula: see text] are *-isomorphic. On each of these planes the Poincaré group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors [Formula: see text]. We show that the *-isomorphism [Formula: see text] also does not map the corresponding twists of the Poincaré group algebra. The quantum field theories on these planes with twisted Poincaré–Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a nontrivial dependence on the noncommutative parameter is present for the Wick–Voros plane in a self-energy diagram whereas it is known to be absent on the Moyal plane (in the absence of gauge fields).1–3 Our results differ from those of Ref. 4 because of differences in the treatments of quantum field theories.

NEW PERTURBATIVE APPROACH TO GENERAL RENORMALIZABLE QUANTUM FIELD THEORIES

1991 ◽  
Vol 06 (19) ◽  
pp. 3381-3397 ◽  
Author(s):  
V. GUPTA ◽  
D.V. SHIRKOV ◽  
O.V. TARASOV
Keyword(s):  
Renormalization Group ◽  
Perturbation Expansion ◽  
Renormalization Scheme ◽  
Coupling Constants ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Coupling Constant ◽  
Perturbative Approach ◽  
Coupling Case

We develop further the new approach to perturbation theory for renormalizable quantum field theories (proposed some years ago) which gives renormalization-scheme-independent predictions for observable quantities. We call the resulting REnormalization-Scheme-Independent PErturba-tion theory RESIPE, for short. First, we formulate explicitly the relation of RESIPE to the renormalization group formalism for the massless one-coupling case. Then we extend this to the case where particle masses cannot be neglected. Further, we generalize the RESIPE formalism for the theory with two coupling constants. A new scheme-invariant perturbation expansion, without reference to renormalization group techniques, is given which is valid for the general case with masses, several kinematic variables and more than one coupling constant. In conclusion, we argue that the appropriately generalized RESIPE provides us with a picture of perturbative predictions, for renormalizable quantum field theories, that is free from regularization and renormalization scheme ambiguities.

scholarly journals Bosonización de líquidos de Luttinger: interacciones con inversión de spin y acoplamiento spin-órbita

2004 ◽  
Author(s):  
◽  
Carlos Aníbal Iucci
Keyword(s):  
Degrees Of Freedom ◽  
Condensed Matter ◽  
Harmonic Approximation ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Spin Orbit ◽  
Luttinger Liquids ◽  
Self Consistent ◽  
Non Local ◽  
Spin Orbit Interactions

In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger liquids. We address the problem of the regularization of the theory. In chapter 4 we treat spin flipping interactions in the non local Thirring model and we obtain an effective bosonic actions that describe separated spin and charge degrees of freedom. In chapter 4 we apply the self consistent harmonic approximation to previously derived bosonic action and we obtain potential depending equations for the spectrum gap. In chapter 5 we include spin-orbit couplings and compute correlations functions. We show that the spin orbit interactions modify the exponents and the phase diagram of the system and makes new susceptibilities diverge for low temperature. Finally in chapter 6 we summarize the main results and the conclusions.

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

scholarly journals Categorification of algebraic quantum field theories

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Universal Algebra ◽  
Finite Groups ◽  
Physical Interpretation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum

AbstractThis paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

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