Quantum field theory in a time-dependent gravitational field

1982 ◽  
Vol 25 (2) ◽  
pp. 365-381 ◽  
Author(s):  
Ikuo Ichinose
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gravitational Field ◽  
Time Dependent ◽  
Quantum Field

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 The Fundamental Discussion between Newton and Einstein

2021 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gravitational Field ◽  
Energy Density ◽  
Speed Of Sound ◽  
Gravitational Energy ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Speed Of Light ◽  
Light Theory

Isaac Newton and Albert Einstein lived in fundamentally different time frames. An interesting question would be: “Who would win the fundamental discussion about the interaction between gravity and light”? Einstein or Newton? Einstein with the fundamental concept of a “curved space-time continuum” within a gravitational field. Or Newton with the fundamental “3rd law of equilibrium between the forces (force-densities)”. It is still the question who was right? Einstein or Newton? Einstein assumes a deformation of the space-time continuum because of a gravitational field. But in general a deformation of any medium will be caused by the change of the energy density within the medium. Like the speed of sound will increase/ decrease when we change the air pressure. However, the speed of sound (which became higher or lower) will still be the same in any direction. The change of the speed of sound will be omni-directional.A gravitational field contains a gravitational energy-density. For that reason the change in the speed of light will be omni-directional within a gravitational field (with a omni-directional gravitational energy density). Einstein however assumes a one-directional change in the speed of light, (only in the direction of the gravitational field). When the change of the speed of light was omni-directional, a beam of light would never be deflected by a gravitational field which is in contradiction with what we measure. Only the absolute value of the speed of light would change omni-directional.The theory of Newton however results in the theory of a 2-directional inertia of photons. The inertia of photons equals zero only in the direction of propagation. Perpendicular to the direction of propagation the mass density of photons is according Einstein’s E = m c^2).The inertia of photons in the direction of propagation will not change within a gravitational field. Gravity can only interact with mass (inertia). Because the mass of the photons in the direction of propagation equals zero, there will ne no interaction with the gravitational field and the photon in the direction of propagation. The speed of light in the direction of propagation will remain unaltered. But according Newton, the photon will have inertia (mass) in the directions perpendicular to the direction of propagation and for that reason the photon will interact with the gravitational field and the photon will be deflected, only in the direction of the gravitational field.And that leads to the consequence that photons will be deflected within a gravitational field when the direction of the gravitational field is perpendicular to the direction of propagation of the photons.To find fundamental mathematical evidence for this concept, we have to make use of Quantum Light Theory. Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.

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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