scholarly journals Higher U(1)-gerbe connections in geometric prequantization

2016 ◽  
Vol 28 (06) ◽  
pp. 1650012 ◽  
Author(s):  
Domenico Fiorenza ◽  
Christopher L. Rogers ◽  
Urs Schreiber
Keyword(s):  
Vector Fields ◽  
Geometric Quantization ◽  
Group Extension ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Hamiltonian Vector Fields ◽  
Principal Connection ◽  
Local Quantum ◽  
Local Observables ◽  
Special Case

We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant–Souriau [Formula: see text]-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the [Formula: see text]-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian [Formula: see text]-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds, we find the [Formula: see text]-algebra extension of Hamiltonian vector fields — which is the higher Poisson bracket of local observables — and show that it is equivalent to the construction proposed by the second author in [Formula: see text]-plectic geometry. Finally, we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.

scholarly journals SCALING ALGEBRAS AND RENORMALIZATION GROUP IN ALGEBRAIC QUANTUM FIELD THEORY

1995 ◽  
Vol 07 (08) ◽  
pp. 1195-1239 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
RAINER VERCH
Keyword(s):  
Renormalization Group ◽  
Scaling Limit ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Systematic Analysis ◽  
Algebraic Quantum ◽  
Local Quantum ◽  
Arbitrary Space ◽  
Local Observables ◽  
Distance Properties

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary space-time manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined.

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 Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories

2019 ◽  
Vol 20 (12) ◽  
pp. 3889-3926
Author(s):  
Henning Bostelmann ◽  
Daniela Cadamuro
Keyword(s):  
Bound States ◽  
Von Neumann Algebras ◽  
Form Factors ◽  
Explicit Construction ◽  
Local Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Von Neumann ◽  
Local Observables ◽  
Wightman Axioms

Abstract We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh–Schlieder property, and in which sense they generate the net of algebras. Our investigation focuses on scalar models without bound states. We establish sufficient criteria for the existence of averaged fields as closable operators, and complete the construction in the specific case of the massive Ising model.

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 A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2022 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
Free Energy ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
Hubble Radius ◽  
The Universe ◽  
Key Parameter ◽  
Do So

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. We do so by defining an appropriate Helmholtz free energy which when extremized relative to a key parameter (the Hubble radius L) provides a scaling formula for the entropy with the Hubble radius (an exponent r used in the text). We deduce that the CKN bound is one possible solution to this extremization problem (with r=3/2), but there are others consistent with r=2. 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.

FOCK SPACE REPRESENTATIONS OF THE ALGEBRA OF DIFFEOMORPHISMS OF THE n-TORUS

1991 ◽  
Vol 06 (05) ◽  
pp. 771-806 ◽  
Author(s):  
FRANCISCO FIGUEIRIDO ◽  
EDUARDO RAMOS
Keyword(s):  
Vector Fields ◽  
Fock Space ◽  
Field Theories ◽  
Bilinear Forms ◽  
Quantum Field Theories ◽  
The Novel ◽  
Quantum Field ◽  
Quantum Fields ◽  
Regularization Procedure ◽  
Group Of Diffeomorphisms

As a first step in the construction of quantum field theories invariant under the group of diffeomorphisms, we obtain Fock space representations of the algebra of vector fields of the n-torus. These representations have the novel feature of being carried by bilinear forms rather than operators. Nevertheless all the usual manipulations can be defined via a suitable regularization procedure. Our approach is a generalization of Kac-Peterson’s method for Diff (S1) which allows us to explicitly construct “quantum fields” transforming as “classical” tensors.

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