An efficient approach for solving Klein–Gordon equation arising in quantum field theory using wavelets

The upper and lower quadrants of flat space-time can be described using the Milne coordinate system. The Klein-Gordon equation of a scalar field in such a coordinate system admits at least two sets of solutions. Based on the Feynman propagator behavior it is shown that only one of the two sets gives the conventional interpretation of quantum field theory, based on a Fock space. Therefore, discarding the other set, one can still keep the Milne coordinate system.

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Introduction

Introduction to Quantum Field Theory with Applications to Quantum Gravity ◽

10.1093/oso/9780198838319.003.0001 ◽

2021 ◽

pp. 3-7

Author(s):

Iosif L. Buchbinder ◽

Ilya L. Shapiro

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Theory ◽

Quantum Gravity ◽

General Notion ◽

Quantum Field ◽

Curved Space ◽

Klein Gordon ◽

Quantized Field ◽

Klein Gordon Equation

This chapter provides an introduction to the book, which addresses the basic notions and fundamental elements of the modern formalism of quantum field theory and presents an introduction to quantum field theory in curved space and quantum gravity. The chapter begins with a discussion of what constitutes a quantum theory and provides some preliminary notes on the topic. It then goes on to outline the structure of the book. The general notion of a quantized field is discussed. In addition, the Klein-Gordon equation, natural units, notations and conventions are introduced.

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

International Journal of Modern Physics D ◽

10.1142/s0218271819440061 ◽

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.

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BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

International Journal of Modern Physics B ◽

10.1142/s0217979212500579 ◽

2012 ◽

Vol 26 (15) ◽

pp. 1250057

Author(s):

HE LI ◽

XIANG-HUA MENG ◽

BO TIAN

Keyword(s):

Field Theory ◽

Bilinear Form ◽

Gordon Equation ◽

Relativistic Quantum ◽

Soliton Solutions ◽

Relativistic Quantum Mechanics ◽

Klein Gordon ◽

Truncated Painlevé Expansion ◽

Klein Gordon Equation ◽

Singular Manifolds

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

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New Exact Solutions for a Generalized Double Sinh-Gordon Equation

Abstract and Applied Analysis ◽

10.1155/2013/268902 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 3

Author(s):

Gabriel Magalakwe ◽

Chaudry Masood Khalique

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Fluid Dynamics ◽

Exact Solutions ◽

Function Method ◽

Gordon Equation ◽

Quantum Field ◽

Integrable Quantum ◽

New Exact Solutions ◽

Integrable Quantum Field Theory

We study a generalized double sinh-Gordon equation, which has applications in various fields, such as fluid dynamics, integrable quantum field theory, and kink dynamics. We employ the Exp-function method to obtain new exact solutions for this generalized double sinh-Gordon equation. This method is important as it gives us new solutions of the generalized double sinh-Gordon equation.

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