Related papers: Conformal field theory complexity from Euler-Arnol…

A comprehensive introduction to two-dimensional conformal field theory is given.

Coherent state path integrals are applied to a many-body problem for non-relativistic electrons in a central potential and an external magnetic field; however, in comparison to previous coherent state path integrals, we definitely fix the…

We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits…

In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In…

In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…

Entanglement is resolved in conformal field theory (CFT) with respect to conformal families to all orders in the UV cutoff. To leading order, symmetry-resolved entanglement is connected to the quantum dimension of a conformal family, while…

We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…

The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…

A systematic formalism for quantum electrodynamics in a classical uniform magnetic field is discussed. The first order radiative correction to the ground state energy of an electron is calculated. This then leads to the anomalous magnetic…

We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…

Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…

We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying…

We derive an entropy formula satisfied by the ground states of 1+1D conformal field theories. The formula implies that the ground state is the critical point of an entropy function. We conjecture that this formula may serve as an…

A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…

To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf…

Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…

We present a classical conformal field theory on an arbitrary two-dimensional spacetime background. The dynamical object is a space-filling string, and the evolution may be thought as occurring on the manifold of the conformal group. The…

We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…

A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local…

Motivated by the idea that consistent quantum field theories should admit a finite description, we investigate the complexity of effective field theories using the framework of effective o-minimality. Our focus is on quantifying the…