scholarly journals General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory

2006 ◽  
Vol 73 (6) ◽  
Author(s):  
Robert Oeckl
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Quantum Field Theory ◽  
General Boundary ◽  
Quantum Field ◽  
Klein Gordon

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.

scholarly journals Linear Yang–Mills Theory as a Homotopy AQFT

2019 ◽  
Vol 378 (1) ◽  
pp. 185-218 ◽  
Author(s):  
Marco Benini ◽  
Simen Bruinsma ◽  
Alexander Schenkel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Poisson Structure ◽  
Gauge Fields ◽  
Quantum Field ◽  
Lorentzian Manifolds ◽  
Algebraic Quantum Field Theory ◽  
Yang Mills ◽  
Algebraic Quantum ◽  
Klein Gordon

AbstractIt is observed that the shifted Poisson structure (antibracket) on the solution complex of Klein–Gordon and linear Yang–Mills theory on globally hyperbolic Lorentzian manifolds admits retarded/advanced trivializations (analogs of retarded/advanced Green’s operators). Quantization of the associated unshifted Poisson structure determines a unique (up to equivalence) homotopy algebraic quantum field theory (AQFT), i.e. a functor that assigns differential graded $$*$$ ∗ -algebras of observables and fulfills homotopical analogs of the AQFT axioms. For Klein–Gordon theory the construction is equivalent to the standard one, while for linear Yang–Mills it is richer and reproduces the BRST/BV field content (gauge fields, ghosts and antifields).

Quantum field theory in phase space

2019 ◽  
Vol 34 (08) ◽  
pp. 1950037 ◽  
Author(s):  
R. G. G. Amorim ◽  
F. C. Khanna ◽  
A. P. C. Malbouisson ◽  
J. M. C. Malbouisson ◽  
A. E. Santana
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Phase Space ◽  
Relativistic Quantum ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Klein Gordon ◽  
Quantization Rules

The tilde conjugation rule in thermofield dynamics, equivalent to the modular conjugation in a [Formula: see text]-algebra, is used to develop unitary representations of the Poincaré group, where the Hilbert space has the phase space content, a symplectic Hilbert space. The state is described by a quasi-amplitude of probability, which is a sort of wave function in phase space, associated with the Wigner function. The quantum field theory in phase space is then constructed, including the quantization rules for the Klein–Gordon and the Dirac fields, the derivation of the electrodynamics in phase space and elements of a relativistic quantum kinetic theory. Towards a physical interpretation of the theory, propagators are associated with the corresponding Wigner functions. The Feynman rules follow accordingly with vertices similar to those of usual non-Abelian quantum field theories.

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