Local and Nonlocal Thermal Field Theory
arXiv:1904.10301
Abstract
Firstly, nonlocal field theories will be motivated, primarily in the gravity sector. We discuss how nonlocal theories of gravity can circumvent typical problems of finitely-many higher derivative theories and can, among other things, be either ghostfree and (potentially) renormalizable and yield a non-singular Newtonian potential. Afterwards we motivate finite temperature field theory, also known as thermal field theory, and study the thermodynamic behavior of both a local and a nonlocal scalar field theory. We compute (primarily leading-order) thermal corrections to the partition function for in low- and high- temperature expansions and calculate the thermal mass which is acquired through continuous interactions with the heat bath. We prove that the nonlocality does not contribute to the partition function of the free nonlocal theory. The presence of the nonlocality can only be noticed through interactions and we conclude that the partition function of the local and the nonlocal scalar theory are fundamentally different when interactions are included. We explain from both a mathematical and physical point of view why the nonlocality can only be noticed at the level of interactions and conclude that this cannot be generalized to arbitrary nonlocal modifications -- only those which do not introduce new poles in the propagator. We study whether our results can be reconciled with the stringy thermal duality and the conjectured Hagedorn phase and conclude that the former is violated, while Hagedorn behavior emerges in the high temperature expansion of the nonlocal scalar theory. We will interpret all these results.
arXiv comment133 pages, 6 figures. arXiv admin note: text overlap with arXiv:1610.08744, arXiv:1704.08674, arXiv:1201.1580, arXiv:1704.07211, arXiv:0910.2274 by other authors
References in corpus (41)
- Noncommutative Field Theory
- Observation of a Centrality-Dependent Dijet Asymmetry in Lead-Lead Collisions at sqrt(S(NN))= 2.76 TeV with the ATLAS Detector at the LHC
- Towards singularity and ghost free theories of gravity
- Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at TeV
- Reconciling dark energy models with f(R) theories
- Super-renormalizable & Finite Gravitational Theories
- Comments on Schnabl's analytic solution for tachyon condensation in Witten's open string field theory
- Non-Local Modification of Gravity and the Cosmological Constant Problem
- Accelerating cosmologies from non-local higher-derivative gravity
- Classical properties of non-local, ghost- and singularity-free gravity
- f(R) gravity theory and CMBR constraints
- Non-perturbative Gravity, Hagedorn Bounce & CMB
- Analytic Solutions for Marginal Deformations in Open String Field Theory
- Self-consistency in Theories with a Minimal Length
- Newtonian limit of nonlocal cosmology
- Behavior of the Newtonian potential for ghost-free gravity and singularity-free gravity
- Ghost conditions for Gauss-Bonnet cosmologies
- Superrenormalizable gauge and gravitational theories
- Ultraviolet Complete Quantum Gravity
- Towards LHC Physics with Non-local Standard Model
- Thermal Duality and Hagedorn Transition from p-adic Strings
- Exorcising the Ostrogradsky ghost in coupled systems
- Hot String Soup
- Nonlocal theories of gravity: the flat space propagator
- Schwarzschild -singularity is not permissible in ghost free quadratic curvature infinite derivative gravity
- Finite Temperature Solitons in Non-Local Field Theories from p-Adic Strings
- An introduction to quantum gravity
- Thermodynamics and Cosmological Constant of Non-Local Field Theories from p-Adic Strings
- Baryon Number Violation
- Rotating metric in Non-Singular Infinite Derivative Theories of Gravity
- Super-Planckian excursions of the inflaton and quantum corrections
- Ultraviolet Complete Electroweak Model Without a Higgs Particle
- An elementary introduction to loop quantum gravity
- Ghost and singularity free theories of gravity
- Thermodynamics of String Field Theory Motivated Nonlocal Models
- A finite electroweak model without a Higgs particle
- Thermal Duality Confronts Entropy: A New Approach to String Thermodynamics?
- Electroweak Model Without A Higgs Particle
- Redesigning Electroweak Theory: Does the Higgs Particle Exist?
- Re-Identifying the Hagedorn Transition
- Euclidean Field Theory