scholarly journals PARTICLE PRODUCTION AND TRANSPLANCKIAN PROBLEM ON THE NONCOMMUTATIVE PLANE

2010 ◽  
Vol 25 (33) ◽  
pp. 2805-2813 ◽  
Author(s):  
MASSIMILIANO RINALDI
Keyword(s):  
Field Theory ◽  
Particle Production ◽  
Number Density ◽  
Commutative Case ◽  
Curved Space ◽  
Equal Time ◽  
Klein Gordon ◽  
Equal Time Commutation ◽  
Suitable Modification ◽  
Noncommutative Plane

We consider the coherent state approach to noncommutativity and we derive from it an effective quantum scalar field theory. We show how the noncommutativity can be taken into account by a suitable modification of the Klein–Gordon product, and of the equal-time commutation relations. We prove that, in curved space, the Bogoliubov coefficients are unchanged, hence the number density of the produced particle is the same as for the commutative case. What changes though is the associated energy density, and this offers a simple solution to the transplanckian problem.

INTERACTING THIRD QUANTIZED GENERAL RELATIVITY AND CHANGE OF TOPOLOGY

1993 ◽  
Vol 08 (20) ◽  
pp. 1849-1858 ◽  
Author(s):  
YOAV PELEG
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Dynamical Equation ◽  
Physical Space ◽  
Positive Definite ◽  
Curved Space ◽  
Infinite Dimensional ◽  
The Third ◽  
Klein Gordon ◽  
Interaction Term

The Wheeler-DeWitt equation can be treated as a dynamical equation of a field theory on superspace, which is a free Klein-Gordon field (in an infinite-dimensional curved space) with a non-positive-definite mass squared term. This suggests that one should add an interaction term to the third quantized theory, and by that to get a Hamiltonian which is bounded from below. This process may allow a change of topology. A consistent third quantized theory can be defined in a subspace of superspace for which the Ricci scalar is zero. We consider a simple example of such subspace, and examine (in it) two kinds of interactions, one which is local in superspace and one which is local in the physical space.

Introduction

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.

NEW CANDIDATES FOR A HERMITIAN APPROACH OF GRAVITY

2013 ◽  
Vol 10 (09) ◽  
pp. 1350041 ◽  
Author(s):  
NICOLETA ALDEA ◽  
GHEORGHE MUNTEANU
Keyword(s):  
Field Theory ◽  
Finsler Geometry ◽  
Finsler Metrics ◽  
Quantum Field ◽  
Schwarzschild Metric ◽  
Curved Space ◽  
Gravitational Fields ◽  
Randers Metric ◽  
Klein Gordon ◽  
Complex Finsler Metrics

In this paper, some possible candidates for the study of gravity are proposed in terms of complex Finsler geometry. These mainly concern the complex Hermitian versions of weakly gravitational metric and Schwarzschild metric. For the weakly gravitational fields, we state few interesting geometrical and physical aspects such as the conditions under which a complex Finsler metrics are projectively related to the weakly gravitational metric. In the Kähler case, the geodesic curves of the weakly gravitational metric are obtained. Some applications concerning the deformations of the weakly gravitational Hermitian metric to a complex Randers metric are described. Another candidate for gravity is given by so-called Hermitian Schwarzschild metric for which some geodesic curves are highlighted. The last part of the paper is devoted to a generalization of the complex Klein–Gordon equations, in terms of Quantum field theory on a curved space.

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.

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

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.

scholarly journals ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Njl Model ◽  
Effective Lagrangian ◽  
Special Solutions ◽  
Curvature Approximation ◽  
Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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