Related papers: Some equivalences between the auxiliary field meth…
Conformal field theory, describing systems with scaling symmetry, plays a crucial role throughout physics. We describe a quantum algorithm to simulate the dynamics of conformal field theories, including the action of local conformal…
In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational…
Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever…
Quantum hardware has the potential to efficiently solve computationally difficult problems in physics and chemistry to reap enormous practical rewards. Analogue quantum simulation accomplishes this by using the dynamics of a controlled…
The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here we introduce the theory and…
Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional…
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive…
Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory…
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to…
Quantum corrections to Legendre transformations are shown to cancel to all orders in supersymmetric theories in path integral formalism. Using this result, lagrangians for auxiliary fields are generalized to non-quadratic forms. In…
The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of…
We develop a new iterative method for finding approximate solutions for spherical bounces associated with the decay of the false vacuum in scalar field theories. The method works for any generic potential in any number of dimensions,…
Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time…
We show that the evolution equation of the effective potential in the auxiliary mass method corresponds to a leading approximation of a certain series. This series is derived from an evolution equation of an effective action using a…
An effective field approximation, similar to the atomic Thomas-Fermi approach, is proposed for studying non-Abelian gauge theories which includes finite-volume effects. As applications of the formalism the equation of state for an SU(2)…
Using the path-integral formalism, we generalize the 't Hooft-Veltman method of unitary regulators to put forward a framework for finite, alternative quantum theories to a given quantum field theory. Feynman-like rules of such a finite,…