scholarly journals Convergence in Quantum Field Theory without Use of Renormalization

2019 ◽  
Author(s):  
Biswaranjan Dikshit
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Electrodynamics ◽  
Ad Hoc ◽  
Probability Amplitude ◽  
Quantum Field ◽  
Counter Term ◽  
Self Energy ◽  
Calculated Probability ◽  
Conventional Methods

In quantum field theory (QFT), it is well known that when Feynman diagrams containing loops are evaluated to account for self interactions, probability amplitude comes out to be infinite which is physically not admissible. So, to make the QFT convergent, various renormalization methods are conventionally followed in which an additional (infinite) counter term is postulated which neutralizes the original infinity generated by diagram. The resulting finite values of amplitudes have agreed with experiments with surprising accuracy. However, proponents of renormalization methods acknowledged that this ad-hoc procedure of subtraction of infinity from infinity to reach at a finite value is not at all satisfactory and there is no physical basis for bringing in the counter term. So, it is desirable to establish a method in QFT which does not generate any infinite term (thus not requiring renormalization), but which predicts same results as conventional methods do. In this paper, we describe such a technique taking self interaction quantum electrodynamics diagram representing electron or photon self energy. In our method, no problem of infinity arises and hence renormalization is not necessary. Still, the dependence of calculated probability amplitude on physical variables in our technique comes out to be same as conventional methods. Using similar procedure, we hope, the problem of non-renormalizability of quantum gravity may be solved in future.

Understanding Phase Transitions in Supersymmetric Quantum Electrodynamics With Resurgence Theory

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Series Expansion ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Perturbative Series

Using resurgence theory to describe phase transitions in quantum field theory shows that information on non-perturbative effects like phase transitions can be obtained from a perturbative series expansion.

STABLE QUASIPARTICLE PICTURE IN THERMAL QUANTUM FIELD PHYSICS

1994 ◽  
Vol 09 (10) ◽  
pp. 1703-1729 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Quantum Field ◽  
Self Energy ◽  
Vector Algebra ◽  
Physical Particle ◽  
Usual Quantum ◽  
Definition Of

It is well known that physical particles are thermally dissipative at finite temperature. In this paper we reformulate both the equilibrium and nonequilibrium thermal field theories in terms of stable quasiparticles. We will redefine the thermal doublets, the double tilde conjugation rules and the thermal Bogoliubov transformations so that our theory can be consistent for most general situations. All operators, including the dissipative physical particle operators, are realized in a Fock space defined by the stable quasiparticles. The propagators of the physical particles are expressed in terms of the operators of such stable quasiparticles, which is a simple diagonal matrix with the diagonal elements being the temporal step functions, same as the propagators in the usual quantum field theory without thermal degrees of freedom. The proper self-energies are also expressed in terms of these stable quasiparticle propagators. This formalism inherits the definition of on-shell self-energy in the usual quantum field theory. With this definition, a self-consistent renormalization is formulated which leads to quantum Boltzmann equation and the entropy law. With the aid of a doublet vector algebra we have an extremely simple recipe for computing Feynman diagrams. We apply this recipe to several examples of equilibrium and nonequilibrium two-point functions, and to the kinetic equation for the particle numbers.

CONSISTENT CHIRAL QUANTUM ELECTRODYNAMICS

1991 ◽  
Vol 06 (14) ◽  
pp. 1299-1304 ◽  
Author(s):  
G. DEMARCO ◽  
C. FOSCO ◽  
R.C. TRINCHERO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Massless Fermions

We construct a unitary and renormalizable quantum field theory in 3+1 dimensions describing the interaction of chiral massless fermions with massive or massless photons.

RELATIVISTIC QUANTUM FIELD THEORY FOR CONDENSED SYSTEMS (II): RENORMALIZATION PROCEDURE

2003 ◽  
Vol 17 (30) ◽  
pp. 5713-5723 ◽  
Author(s):  
HIROYUKI MATSUURA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Electric Charge ◽  
Relativistic Quantum ◽  
Free Field ◽  
Mass Shift ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Self Energy ◽  
Physical Mass

We proposed Atomic Schwinger–Dyson method (ASD method) in previous paper, which was a nonperturbative and relativistic quantum field theory for a finite baryon density. We think it is important to show the significance of renormarization in order to get real physical predictions. Moreover, the real value of physical mass, electric charge and wave function are completely different from those of the non-renormalized electron and photon in mean field theory, since there are many of the particle-antiparticle creations and annihilations, particle-hole excitation, and Pauli blocking, which give an effect on bare mass, electric charge, polarization of vacuum, and self-energy. In this paper, we shows that ASD method is renormalizable theory, and that photon condensation of ASD method gave rise to Coulomb's potential and the mass shift of electron. The interacting photon and electron fields, which have physical mass and electric charge, are expressed as generalized free field equations by using the mass shift and the self-energy of those particles. We obtain the expression of an exact solution of these particles on the basis of the Green functional method.

scholarly journals Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 43 ◽  
Author(s):  
Akihiro Nishiyama ◽  
Shigenori Tanaka ◽  
Jack A. Tuszynski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Time Evolution ◽  
Central Region ◽  
Quantum Electrodynamics ◽  
Quantum Tunneling ◽  
Evolution Equations ◽  
Open Systems ◽  
Quantum Field ◽  
The Brain

We derive time evolution equations, namely the Klein–Gordon equations for coherent fields and the Kadanoff–Baym equations in quantum electrodynamics (QED) for open systems (with a central region and two reservoirs) as a practical model of quantum field theory of the brain. Next, we introduce a kinetic entropy current and show the H-theorem in the Hartree–Fock approximation with the leading-order (LO) tunneling variable expansion in the 1st order approximation for the gradient expansion. Finally, we find the total conserved energy and the potential energy for time evolution equations in a spatially homogeneous system. We derive the Josephson current due to quantum tunneling between neighbouring regions by starting with the two-particle irreducible effective action technique. As an example of potential applications, we can analyze microtubules coupled to a water battery surrounded by a biochemical energy supply. Our approach can be also applied to the information transfer between two coherent regions via microtubules or that in networks (the central region and the N res reservoirs) with the presence of quantum tunneling.

scholarly journals The principle of stationary variance in quantum field theory

2014 ◽  
Vol 29 (05) ◽  
pp. 1450026 ◽  
Author(s):  
Fabio Siringo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum System ◽  
Quantum Electrodynamics ◽  
Best Approximation ◽  
Variational Approach ◽  
Heisenberg Model ◽  
Gauge Theories ◽  
Quantum Field

The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.

Quantum electrodynamics and Hilbert space theory

1956 ◽  
Vol 52 (4) ◽  
pp. 719-733
Author(s):  
J. G. Taylor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Space Theory ◽  
Electrons And Positrons ◽  
Simple Quantum ◽  
Interacting Electrons ◽  
Space Formalism

ABSTRACTThis paper describes an attempt to formulate quantum field theory, in particular quantum electrodynamics, in terms of Hilbert space theory. The work of Cook (1) is extended to give a precise description of non-interacting electrons and positrons. The hole interpretation is not required in this extension, and no subtraction formalism is required. It is shown that the formalism can never reduce to that of intuitive quantum field theory except by an abuse of language associated with the δ-function. Interaction cannot be introduced in a simple manner into the rigorous formalism, so it seems extremely difficult to develop the Hilbert space formalism for quantum field theory in any useful manner.These difficulties indicate that an investigation of the Hilbert space basis of simple quantum theory is necessary before a rigorous mathematical formalism for intuitive quantum field theory can be developed.

scholarly journals Quantum spectral dimension in quantum field theory

2016 ◽  
Vol 25 (05) ◽  
pp. 1650058 ◽  
Author(s):  
Gianluca Calcagni ◽  
Leonardo Modesto ◽  
Giuseppe Nardelli
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Transition Amplitude ◽  
Energy Transition ◽  
Dispersion Relations ◽  
Spectral Dimension ◽  
Quantum Field ◽  
Self Energy ◽  
Dimension Formula ◽  
A Value

We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension [Formula: see text] of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension [Formula: see text]. In particular, in the presence of higher momentum powers it changes with the scale, dropping from [Formula: see text] in the infrared (IR) to a value [Formula: see text] in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value [Formula: see text] for any dimension [Formula: see text].

scholarly journals MONTE CARLO CALCULATION OF THE LATERAL CASIMIR FORCES BETWEEN RECTANGULAR GRATINGS WITHIN THE FORMALISM OF LATTICE QUANTUM FIELD THEORY

2011 ◽  
Vol 26 (16) ◽  
pp. 2743-2756 ◽  
Author(s):  
OLEG PAVLOVSKY ◽  
MAXIM ULYBYSHEV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Lattice Quantum Field Theory ◽  
Quantum Electrodynamics ◽  
Monte Carlo Calculation ◽  
Quantum Field ◽  
Casimir Forces ◽  
Lattice Quantum

We propose a new Monte Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.

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