Quantum theory of free scalar fields

2012 ◽  
pp. 8-16
Author(s):  
Tom Banks
Keyword(s):  
Quantum Theory ◽  
Scalar Fields ◽  
Free Scalar

Functional Quantum Theory of Free Relativistic Scalar Fields

1971 ◽  
Vol 26 (9) ◽  
pp. 1553-1558 ◽  
Author(s):  
W. Bauhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Functional Equations ◽  
Scalar Product ◽  
Functional Space ◽  
Scalar Fields ◽  
Quantum Field ◽  
Isometric Mapping ◽  
Free Scalar

Abstract Dynamics of quantum field theory can be formulated by functional equations. Starting with the Schwinger functionals of the free scalar field, functional equations and corresponding many particle functionals are derived. To establish a complete functional quantum theory, a scalar product in functional space has to be defined as an isometric mapping of physical Hilbert space into the functional space.

scholarly journals Quantization of Free Scalar Fields in the Presence of Natural Cutoffs

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
K. Nozari ◽  
F. Moafi ◽  
F. Rezaee Balef
Keyword(s):  
Quantum Theory ◽  
Path Integral ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Scalar Fields ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Higher Dimensional ◽  
Free Scalar ◽  
Maximal Momentum

We construct a quantum theory of free scalar fields in (1+1)-dimensions based on the deformed Heisenberg algebrax^,p^=iħ1-βp+2β2p2, that admits the existence of both a minimal measurable length and a maximal momentum, whereβis a deformation parameter. We consider both canonical and path integral formalisms of the scenario. Finally a higher dimensional extension is easily performed in the path integral formalism.

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

Canonical quantization of free fields

2021 ◽  
pp. 70-98
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Electromagnetic Fields ◽  
Classical Theory ◽  
Canonical Quantization ◽  
Classical Mechanics ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Spinor Fields ◽  
Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

scholarly journals Free Scalar Fields in Finite Volume Are Holographic

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 223
Author(s):  
Csaba Balázs
Keyword(s):  
Scalar Field ◽  
Surface Area ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Flat Space ◽  
Linear Size ◽  
Energy Mode ◽  
Free Scalar ◽  
Quantized Field

This brief note presents a back-of-the-envelope calculation showing that the number of degrees of freedom of a free scalar field in expanding flat space equals the surface area of the Hubble volume in Planck units. The logic of the calculation is the following. The amount of energy in the Hubble volume scales with its linear size, consequently the volume can only contain a finite number of quantized field modes. Since the momentum of the lowest energy mode scales inversely with the linear size of the volume, the maximal number of such modes in the volume scales with its surface area. It is possible to show that when the number of field modes is saturated the modes are confined to the surface of the volume. Gravity only enters this calculation as a regulator, providing a finite volume that contains the field, the entire calculation is done in flat space. While this toy model is bound to be incomplete, it is potentially interesting because it reproduces the defining aspects of holography, and advocates a regularization of the quantum degrees of freedom based on Friedmann’s equation.

Free Scalar Fields

2016 ◽  
pp. 17-39
Author(s):  
Mikko Laine ◽  
Aleksi Vuorinen
Keyword(s):  
Scalar Fields ◽  
Free Scalar

scholarly journals κ-DEFORMED STATISTICS AND CLASSICAL FOUR-MOMENTUM ADDITION LAW

2008 ◽  
Vol 23 (09) ◽  
pp. 653-665 ◽  
Author(s):  
MARCIN DASZKIEWICZ ◽  
JERZY LUKIERSKI ◽  
MARIUSZ WORONOWICZ
Keyword(s):  
Minkowski Space ◽  
Fock Space ◽  
Scalar Fields ◽  
Cross Product ◽  
Creation And Annihilation Operators ◽  
Multiplication Rule ◽  
Symmetry Properties ◽  
Deformed Algebra ◽  
Free Scalar

We consider κ-deformed relativistic symmetries described algebraically by modified Majid–Ruegg bi-cross-product basis and investigate the quantization of field oscillators for the κ-deformed free scalar fields on κ-Minkowski space. By modification of standard multiplication rule, we postulate the κ-deformed algebra of bosonic creation and annihilation operators. Our algebra permits one to define the n-particle states with classical addition law for the four-momentum in a way which is not in contradiction with the nonsymmetric quantum four-momentum co-product. We introduce κ-deformed Fock space generated by our κ-deformed oscillators which satisfy the standard algebraic relations with modified κ-multiplication rule. We show that such a κ-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of κ-deformed algebra of oscillators in field-theoretic noncommutative framework.

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