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 How low can vacuum energy go when your fields are finite-dimensional?

2019 ◽  
Vol 28 (14) ◽  
pp. 1944006
Author(s):  
ChunJun Cao ◽  
Aidan Chatwin-Davies ◽  
Ashmeet Singh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Quantum Field ◽  
Locally Finite ◽  
Finite Dimensional ◽  
Finite Dimensionality ◽  
Klein Gordon ◽  
Dimensional Version

According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this paper, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein–Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.

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 ISSUES WITH VACUUM ENERGY AS THE ORIGIN OF DARK ENERGY

2012 ◽  
Vol 27 (27) ◽  
pp. 1250154 ◽  
Author(s):  
HOURI ZIAEEPOUR
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dark Energy ◽  
Particle Physics ◽  
Vacuum Energy ◽  
A Priori ◽  
Higgs Field ◽  
Scalar Fields ◽  
Vacuum Energy Density ◽  
Quantum Field

In this paper, we address some of the issues raised in the literature about the conflict between a large vacuum energy density, a priori predicted by quantum field theory, and the observed dark energy which must be the energy of vacuum or include it. We present a number of arguments against this claim and in favor of a null vacuum energy. They are based on the following arguments: A new definition for the vacuum in quantum field theory as a frame-independent coherent state; results from a detailed study of condensation of scalar fields in Friedmann–Lemaître–Robertson–Walker (FLRW) background performed in a previous work; and our present knowledge about the Standard Model of particle physics. One of the predictions of these arguments is the confinement of nonzero expectation value of Higgs field to scales roughly comparable with the width of electroweak gauge bosons or shorter. If the observation of Higgs by the LHC is confirmed, accumulation of relevant events and their energy dependence in near future should allow us to measure the spatial extend of the Higgs condensate.

scholarly journals Axion–photon mixing in quantum field theory and vacuum energy

2019 ◽  
Vol 790 ◽  
pp. 427-435 ◽  
Author(s):  
A. Capolupo ◽  
I. De Martino ◽  
G. Lambiase ◽  
An. Stabile
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Energy ◽  
Quantum Field

scholarly journals Some remarks on Dirac's hole theory versus quantum field theory

2003 ◽  
Vol 81 (10) ◽  
pp. 1165-1175 ◽  
Author(s):  
D Solomon
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Hole Theory ◽  
Theory Versus

Dirac's hole theory and quantum field theory are generally considered to be equivalent to each other. However, it has been recently shown that this is not necessarily the case. In this article, we will discuss the reason for this lack of equivalence and suggest a possible solution.PACS Nos.: 03.65.–w, 11.10.–z

scholarly journals Dirac's hole theory versus quantum field theory

2002 ◽  
Vol 80 (8) ◽  
pp. 837-845 ◽  
Author(s):  
F AB Coutinho ◽  
D Kiang ◽  
Y Nogami ◽  
L Tomio
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Pauli Principle ◽  
Quantum Field ◽  
Hole Theory ◽  
Intermediate States ◽  
Theory Versus

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. The equivalence, however, does not necessarily hold, as we discuss in terms of models of a certain type. We further suggest that the equivalence may fail in more general models. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory. PACS Nos.: 03.65-w, 11.10-z, 11.15Bt, 12.39Ba

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