Renormalizability of the time-dependent variational equations in quantum field theory

1987 ◽  
Vol 36 (10) ◽  
pp. 3128-3137 ◽  
Author(s):  
So-Young Pi ◽  
M. Samiullah
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Time Dependent ◽  
Quantum Field ◽  
Variational Equations

A UNIFIED FORMALISM OF THERMAL QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (14) ◽  
pp. 2363-2409 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Polarization ◽  
Time Dependent ◽  
Quantum Field ◽  
Bogoliubov Transformation ◽  
Transformation Matrices ◽  
Thermo Field Dynamics ◽  
The Matrix ◽  
Recent Developments

We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.

scholarly journals Some differences between Dirac's hole theory and quantum field theory

2005 ◽  
Vol 83 (3) ◽  
pp. 257-271 ◽  
Author(s):  
Dan Solomon
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Exact Solution ◽  
Dirac Equation ◽  
Vacuum Energy ◽  
Time Dependent ◽  
Quantum Field ◽  
Hole Theory

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered equivalent. However, it was recently shown by several investigators that this is not necessarily the case because when the change in the vacuum energy was calculated for a time-independent perturbation, HT and QFT yielded different results. In this paper, we extend this discussion to include a time-dependent perturbation for which the exact solution to the Dirac equation is known. We show that for this case also, HT and QFT yield different results. In addition, we offer some discussion of the problem of anomalies in QFT. PACS Nos.: 03.65–w, 11.10–z

scholarly journals Classical limit of time-dependent quantum field theory — a Schwinger–Dyson approach

2001 ◽  
Vol 515 (3-4) ◽  
pp. 463-469 ◽  
Author(s):  
Fred Cooper ◽  
Avinash Khare ◽  
Harvey Rose
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Classical Limit ◽  
Time Dependent ◽  
Quantum Field

scholarly journals Quantum unitary dynamics of a charged fermionic field and Schwinger effect

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Álvaro Álvarez-Domínguez ◽  
Luis J. Garay ◽  
David García-Heredia ◽  
Mercedes Martín-Benito
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Particle Creation ◽  
Vacuum State ◽  
Time Dependent ◽  
Quantum Field ◽  
Homogeneous Electric Field ◽  
Fermionic Field ◽  
Translational Invariance ◽  
Definition Of

Abstract In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In cosmological backgrounds this ambiguity has been reduced by imposing that the quantization preserves the symmetries of the system and that the dynamics is unitarily implemented. In this work, we apply these requirements to the quantization of a massive charged fermionic field coupled to a classical time-dependent homogeneous electric field, extending previous studies done for a scalar field. We characterize the quantizations fulfilling the criteria above and we show that they form a unique equivalence class of unitarily related quantizations, which provide a well-defined number of created particles at all finite times.

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