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Using the parametrised representation of field theory (in which the location in spacetime of a part of a field is itself represented by a map from the base manifold to Minkowski spacetime) I demonstrate that in both local and global cases,…

General Relativity and Quantum Cosmology · Physics 2015-02-24 David Wallace

Modern relativistic theory of the second quantization of fermion and boson fields is based on the use of the mathematical apparatus of C*-algebras and Lie superalgebras. In this case, for fermions, the Lorentz transformations are considered…

General Physics · Physics 2018-08-15 V. V. Monakhov

We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first…

High Energy Physics - Theory · Physics 2023-09-06 Sze-Shiang Feng

We develop a new mathematical approach to diffeomorphism invariant quantum states for the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators…

Mathematical Physics · Physics 2017-10-31 James Moffat , Teodora Oniga , Charles H. -T. Wang

In this paper, we introduce C*-algebraic partial compact quantum groups, which are quantizations of topological groupoids with discrete object set and compact morphism spaces. These C*-algebraic partial compact quantum groups are…

Operator Algebras · Mathematics 2019-01-29 Kenny De Commer

Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the…

General Relativity and Quantum Cosmology · Physics 2016-07-21 Mohammad Vahid Takook

Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…

Mathematical Physics · Physics 2024-07-03 Kilian Hersent

In this paper we study the quantisation of scalar field theory in $\kappa$-deformed space-time. Using a quantisation scheme that use only field equations, we derive the quantisation rules for deformed scalar theory, starting from the…

High Energy Physics - Theory · Physics 2019-09-23 E. Harikumar , Vishnu Rajagopal

We employ the Dirac procedure to quantize the self-dual massive Kalb-Ramond-Klein-Gordon model in $2+1$ dimensional spacetimes. The canonical fields are expressed in terms of $2$-surfaces and signed points, ensuring the automatic…

High Energy Physics - Theory · Physics 2025-05-29 E. Iñiguez , M. Freire , L. Leal , E. Contreras

The conventional role of spacetime geometry in the description of gravity is pointed out. Global Poincar$\acute{\mbox{e}}$ symmetry as an inner symmetry of field theories defined on a fixed Minkowski spacetime is discussed. Its extension to…

General Relativity and Quantum Cosmology · Physics 2007-05-23 C. Wiesendanger

Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is…

High Energy Physics - Theory · Physics 2021-11-12 Daniele Colosi , Robert Oeckl

Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…

High Energy Physics - Theory · Physics 2011-07-19 Richard J. Szabo

Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients, isomorphic $\mathcal{G}_{1,4}$. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper…

General Mathematics · Mathematics 2007-05-23 Jose B. Almeida

Let $G$ be a locally compact abelian Hausdorff topological group which is non-compact and whose Pontryagin dual $\Gamma$ is partially ordered. Let $\Gamma^{+}\subset\Gamma$ be the semigroup of positive elements in $\Gamma$. The Hardy space…

Operator Algebras · Mathematics 2015-08-21 Uğur Gül

We propose a definition of compact quantum groupoids in the setting of C*-algebras, associate to such a quantum groupoid a regular C*-pseudo-multiplicative unitary, and use this unitary to construct a dual Hopf C*-bimodule and to pass to a…

Operator Algebras · Mathematics 2013-07-02 Thomas Timmermann

Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…

We study the mathematical structure of the notion of measurement space, which extends aspects of noncommutative topology that are based on quantale theory. This yields a geometric model of physical measurements that provides a realist…

Mathematical Physics · Physics 2023-01-10 Pedro Resende

The Clifford algebra, generated by the real (Majorana) gamma-matrices and by a hermitian gamma_5, gives room to the reductive Lie algebra u(2,2) of the conformal group extended by the u(1) helicity operator. Its unitary positive energy…

Mathematical Physics · Physics 2019-05-31 Ivan Todorov

As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…

High Energy Physics - Theory · Physics 2023-09-06 Sze-Shiang Feng , Mogus Mochena

There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…

Operator Algebras · Mathematics 2024-07-19 Petr Ivankov