scholarly journals GRAVITATIONAL RENORMALIZATION OF QUANTUM FIELD THEORY

2012 ◽  
Vol 27 (32) ◽  
pp. 1250186 ◽  
Author(s):  
ROBERTO CASADIO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Feynman Graph ◽  
The Other ◽  
Quantum Field ◽  
High Momentum ◽  
Feynman Propagator ◽  
Virtual Particle ◽  
Virtual Particles

We propose to include gravity in quantum field theory nonperturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space–time determined by the four-momenta of the other particles in the same graph. By making additional working assumptions, we are able to put this idea at work in a simplified context, and obtain a modified Feynman propagator for the massless neutral scalar field. Our expression shows a suppression at high momentum, strong enough to entail finite results, to all loop orders, for processes involving at least two virtual particles.

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 SHORT DISTANCE PROPERTIES FROM LARGE DISTANCE BEHAVIOR

1998 ◽  
Vol 13 (23) ◽  
pp. 4101-4122 ◽  
Author(s):  
PAUL MANSFIELD ◽  
MARCOS SAMPAIO ◽  
JIANNIS PACHOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Large Distance ◽  
Short Distance ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Expansion Coefficients ◽  
Distance Behavior ◽  
Distance Properties

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficients can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counterterms. We also describe an approximate simplification that occurs for the sine–Gordon and sinh–Gordon vacuum functionals.

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

scholarly journals A NONASSOCIATIVE QUATERNION SCALAR FIELD THEORY

2013 ◽  
Vol 28 (35) ◽  
pp. 1350163 ◽  
Author(s):  
SERGIO GIARDINO ◽  
PAULO TEOTÔNIO-SOBRINHO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
String Theory ◽  
Hopf Algebra ◽  
Scalar Product ◽  
Quantum Field ◽  
Quantum Algebras ◽  
Function Algebras ◽  
Nonlinear Quantum

A nonassociative Groenewold–Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and nonlinear quantum field theory.

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.

scholarly journals Diagrammar of physical and fake particles and spectral optical theorem

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Damiano Anselmi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Optical Theorem ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Virtual Particles ◽  
Major Significance ◽  
Algebraic Operations

Abstract We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to “skeleton” diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with “diagonal”, box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles.

Metastable vacua in quantum field theory (QFT)

2021 ◽  
pp. 919-941
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Imaginary Part ◽  
Classical Limit ◽  
Three Dimensions ◽  
Quantum Field ◽  
Field Equations ◽  
Barrier Penetration ◽  
General Scalar

The methods to evaluate barrier penetration effects, in the semi-classical limit are generalized to quantum field theory (QFT). Since barrier penetration is associated with classical motion in imaginary time, the QFT is considered in its Euclidean formulation. In the representation of QFT in terms of field integrals, in the semi-classical limit, barrier penetration is related to finite action solutions (instantons) of the classical field equations. The evaluation of instanton contributions at leading order is explained, the main new problem arising from ultraviolet divergences. The lifetime of metastable states is related to the imaginary part of the ‘ground state’ energy. However, for later purpose, it is useful to calculate the imaginary part not only of the vacuum amplitude, but also of correlation functions. In the case of the vacuum amplitude, the instanton contribution is proportional to the space–time volume. Therefore, dividing by the volume, one obtains the probability per unit time and unit volume of a metastable pseudo-vacuum to decay. A scalar field theory with a φ4 interaction, generalization of the quartic anharmonic oscillator is discussed in two and three dimensions, dimensions in which the theory is super-renormalizable, then more general scalar field theories are considered.

‘In the Light of Leibniz and Lucretius’: An Encounter between Deleuze and New Materialism

2021 ◽  
Vol 15 (4) ◽  
pp. 497-522
Author(s):  
Hanjo Berressem
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Physics ◽  
New Materialism ◽  
Quantum Field ◽  
Virtual Particles ◽  
Continuity And Discontinuity

While most new materialists, including Thomas Nail, tend to distance themselves from Deleuze, this essay reads the encounter of Nail's ‘process materialism’ and Deleuzian philosophy as productive rather than contentious. After tracing the affinities of their notions of continuity and discontinuity by way of Deleuze's The Fold: Leibniz and the Baroque and Nail's Lucretius I: An Ontology of Motion and Being and Motion, the essay considers Nail's unfolding of Lucretius’ luminous philosophy in relation to Deleuze's reading of Lucretius from within Deleuze's own ‘philosophical luminism’. Within the multiple overlaps between Nail and Deleuze, particularly vis-à-vis quantum physics and quantum field theory, their divergent readings of the particle–wave duality bring about a productive conceptual tension. Nail's argument about the ontological precedence of waves over particles (‘process precedes existence’) is illuminated by Deleuze's concept of their ontological complementarity (actual particles and virtual waves, virtual particles and actual waves), and vice versa.

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