scholarly journals OPE for XXX

2018 ◽  
Vol 30 (06) ◽  
pp. 1840006 ◽  
Author(s):  
Philippe Di Francesco ◽  
Fedor Smirnov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Experimental Data ◽  
Correlation Functions ◽  
Spin Chain ◽  
Operator Product Expansion ◽  
The Other ◽  
Operator Product ◽  
Quantum Field ◽  
Xxx Model

We explain a new method for finding the correlation functions for the XXX model which is based on the concepts of Operator Product Expansion of Quantum Field Theory on one hand and of fermionic bases for the XXX spin chain on the other. With this method, we are able to perform computations for up to 11 lattice sites. We show that these “experimental” data allow to guess exact formulae for the OPE coefficients. In memory of Ludwig Dmitrievich Faddeev

Dynamical derivation of vacuum operator-product expansion in Euclidean conformal quantum field theory

1976 ◽  
Vol 13 (4) ◽  
pp. 887-912 ◽  
Author(s):  
V. K. Dobrev ◽  
V. B. Petkova ◽  
S. G. Petrova ◽  
I. T. Todorov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Quantum Field

scholarly journals QUANTUM FIELD THEORY IN CURVED SPACE–TIME, THE OPERATOR PRODUCT EXPANSION, AND DARK ENERGY

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2607-2615 ◽  
Author(s):  
STEFAN HOLLANDS ◽  
ROBERT M. WALD
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Operator Product Expansion ◽  
Vacuum Expectation ◽  
Vacuum State ◽  
Space Time ◽  
Operator Product ◽  
Energy Tensor ◽  
Quantum Field ◽  
Curved Space

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved space–time, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved space–time does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a "vacuum state" and "particles". We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients — and, thus, the quantum field theory. By contrast, ground/vacuum states — in space–times, such as Minkowski space–time, where they may be defined — cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory.

THE CLASSICAL HARMONIC OSCILLATOR ON GALOIS AND P-ADIC FIELDS

1989 ◽  
Vol 04 (09) ◽  
pp. 2211-2233 ◽  
Author(s):  
YANNICK MEURICE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Difference Equation ◽  
Harmonic Oscillator ◽  
Continuum Limit ◽  
The Other ◽  
Quantum Field ◽  
Real Numbers ◽  
Technical Tool ◽  
Classical Motion

Starting from a difference equation corresponding to the harmonic oscillator, we discuss various properties of the classical motion (cycles, conserved quantity, boundedness, continuum limit) when the dynamical variables take their values on Galois or p-adic fields. We show that these properties can be applied as a technical tool to calculate the motion on the real numbers. On the other hand, we also give an example where the motions over Galois and p-adic fields have a direct physical interpretation. Some perspectives for quantum field theory and strings are briefly discussed.

scholarly journals Connected Chord Diagrams and Bridgeless Maps

10.37236/7400 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Julien Courtiel ◽  
Karen Yeats ◽  
Noam Zeilberger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lambda Calculus ◽  
The Other ◽  
Combinatorial Proof ◽  
Quantum Field ◽  
Technical Parameter ◽  
Simple Application ◽  
Chord Diagrams ◽  
Combinatorial Maps

We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We describe a bijection between these two classes, which naturally extends to indecomposable diagrams and general rooted maps. As an application, this bijection provides a simplifying framework for some technical quantum field theory work realized by some of the authors. Most notably, an important but technical parameter naturally translates to vertices at the level of maps. We also give a combinatorial proof to a formula which previously resulted from a technical recurrence, and with similar ideas we prove a conjecture of Hihn. Independently, we revisit an equation due to Arquès and Béraud for the generating function counting rooted maps with respect to edges and vertices, giving a new bijective interpretation of this equation directly on indecomposable chord diagrams, which moreover can be specialized to connected diagrams and refined to incorporate the number of crossings. Finally, we explain how these results have a simple application to the combinatorics of lambda calculus, verifying the conjecture that a certain natural family of lambda terms is equinumerous with bridgeless maps.

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