Related papers: Introduction to spherical field theory
The truncated 4-dimensional sphere $S^4$ and the action of the self-interacting scalar field on it are constructed. The path integral quantization is performed while simultaneously keeping the SO(5) symmetry and the finite number of degrees…
Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on an N-dimensional lattice, which is, in most cases, computationally quite the challenging task even with…
The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation,…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available…
Quantum field theory is used to describe the contribution of possible new QCD vacuum replica to hadronic processes. This sigma-like new state has been recently shown to be likely to appear for any realistic four-quark interaction kernel as…
We study the second quantization of field theory on the q-deformed fuzzy sphere for real q. This is performed using a path-integral over the modes, which generate a quasiassociative algebra. The resulting models have a manifest U_q(su(2))…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be…
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working…
We begin with a description of spacetime by a 4-dimensional cubic lattice $\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\sscripthat$…
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…
A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical…
We present a quantum-field-theoretic treatment of massive chiral fields in which particles possess well-defined chirality and helicity. This framework reproduces the chiral oscillation formula previously obtained in first-quantized…
Scalar field theory is studied by constructing interacting saddle point expansions in the symmetric and broken phase, respectively. Focusing on analytically tractable saddle expansions, it is found that broken and symmetric phases are…
We propose a new polymerization scheme for scalar fields coupled to gravity. It has the advantage of being a (non-bijective) canonical transformation of the fields and therefore ensures the covariance of the theory. We study it in detail in…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a…