Related papers: Worldline Formalism and Noncommutative Theories
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom. In a first quantized formalism, $\theta^{\mu\nu}$ and its canonical…
In [arXiv:1004.2488], Baumann et al. present a new formalism for studying cosmological systems where the characteristic scale of non-linearities is much smaller than the Hubble scale. By integrating out the short-wavelength modes, it is…
We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop…
We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying…
This thesis examines low-energy effective actions of supersymmetric quantum field theories. These actions contain information about the low-energy field content and dynamics of quantum field theories and are essential for understanding…
We use the worldline formalism to derive a universal relation for the lower boundary of the conformal window in non-supersymmetric QCD-like theories. The derivation relies on the convergence of the expansion of the fermionic determinant in…
The spherical field formalism---a nonperturbative approach to quantum field theory---was recently introduced and applied to phi^4 theory in two dimensions. The spherical field method reduces a quantum field theory to a finite-dimensional…
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical…
We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
The problem of non-linear transport near a quantum phase transition is solved within the Landau theory for the dissipative insulator-superconductor phase transition in two dimensions. Using the non-equilibrium Schwinger round-trip Green…
We present a unified approach to holomorphic anomaly equations and some well-known quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the Deligne-Mumford moduli spaces…
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts. Firstly as field theories on noncommutative spacetimes they come with natural…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…