scholarly journals Non-unitarity of Minkowskian non-local quantum field theories

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Fabio Briscese ◽  
Leonardo Modesto
Keyword(s):  
Scalar Field ◽  
Imaginary Part ◽  
Local Field ◽  
Field Theories ◽  
Unitarity Condition ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Not Given ◽  
Local Quantum ◽  
Non Local

AbstractWe show that Minkowskian non-local quantum field theories are not unitary. We consider a simple one loop diagram for a scalar non-local field and show that the imaginary part of the corresponding complex amplitude is not given by Cutkosky rules, indeed this diagram violates the unitarity condition. We compare this result with the case of an Euclidean non-local scalar field, that has been shown to satisfy the Cutkosky rules, and we clearly identify the reason of the breaking of unitarity of the Minkowskian theory.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

RAINBOW STATISTICS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4623-4641 ◽  
Author(s):  
MICHELE ARZANO ◽  
DARIO BENEDETTI
Keyword(s):  
Quantum Group ◽  
Hilbert Spaces ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Local Quantum ◽  
Group Symmetries ◽  
Noncommutative Quantum

Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

scholarly journals On the renormalization of entanglement entropy

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Jin-Yi Pang ◽  
Jiunn-Wei Chen
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Scalar Field ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Replica Trick ◽  
Dimensional Spacetime

AbstractThe renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.

scholarly journals ANGULAR INTRICACIES IN HOT GAUGE FIELD THEORIES

2005 ◽  
Vol 20 (19) ◽  
pp. 4412-4418
Author(s):  
T. GRANDOU
Keyword(s):  
Gauge Field ◽  
Imaginary Part ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Leading Order ◽  
Singularity Problem ◽  
Collinear Singularity ◽  
Definite Sequence

In hot quantum field theories, "Hard Thermal Loops" leading order calculations call for a definite sequence of angular averages and discontinuity (or Imaginary part prescription) operations, and run otherwise into incorrect results. The ten years old collinear singularity problem of hot QCD, provides a dramatic illustration of that fate.

scholarly journals Renormalization in Combinatorially Non-Local Field Theories: The Hopf Algebra of 2-Graphs

2021 ◽  
Vol 24 (2) ◽  
Author(s):  
Johannes Thürigen
Keyword(s):  
Hopf Algebra ◽  
Local Field ◽  
Broad Class ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field ◽  
Random Geometry ◽  
Perturbative Renormalization ◽  
Non Local ◽  
Perturbative Quantum

AbstractRenormalization in perturbative quantum field theory is based on a Hopf algebra of Feynman diagrams. A precondition for this is locality. Therefore one might suspect that non-local field theories such as matrix or tensor field theories cannot benefit from a similar algebraic understanding. Here I show that, on the contrary, perturbative renormalization of a broad class of such field theories is based in the same way on a Hopf algebra. Their interaction vertices have the structure of graphs. This gives the necessary concept of locality and leads to Feynman diagrams defined as “2-graphs” which generate the Hopf algebra. These results set the stage for a systematic study of perturbative renormalization as well as non-perturbative aspects, e.g. Dyson-Schwinger equations, for a number of combinatorially non-local field theories with possible applications to random geometry and quantum gravity.

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