Related papers: Nonlinear soft mode action for the large-$p$ SYK m…
On an interval compactification in supersymmetric theory, boundary conditions for bulk fields must be treated carefully. If they are taken arbitrarily following the requirement that a theory is supersymmetric, the conditions could give…
We recently introduced a robust approach to the derivation of sharp asymptotic formula for correlation functions of statistical mechanics models in the high-temperature regime. We describe its application to the nonperturbative proof of…
We build a statistical description of fermions, taking into account the spin degree of freedom in addition to the momentum of particles, and we detail its use in the context of the kinetic theory of gases of fermions particles. We show that…
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields.…
The fixed point actions for Wilson and staggered lattice fermions are determined by iterating renormalization group transformations. In both cases a line of fixed points is found. Some points have very local fixed point actions. They can be…
We show that a random interacting model exhibits solvable non-Fermi liquid behavior and exotic pairing behavior. This model, dubbed as the Yukawa-SYK model, describes the random Yukawa coupling between $M$ quantum dots each hosting $N$…
It is shown how to solve the Euclidean equations of motion of a point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective…
The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic…
Motivated by the problem of N coupled Hubbard chains, we investigate a generalisation of the Schulz-Shastry model containing two species of one-dimensional fermions interacting via a gauge field that depends on the positions of all the…
After a brief survey of effective field theories, the linear sigma model is discussed as a prototype of an effective field theory of the standard model below the chiral-symmetry-breaking scale. Although it can serve as a toy model for the…
The action potential constitutes the digital component of the signaling dynamics of neurons. But the biophysical nature of the full-time course of the action potential associated with changes in membrane potential is mathematically distinct…
We analyze the soft supersymmetry breaking parameters obtained in grand unified theories after integrating out the heavy GUT-states. The superfield formalism greatly simplifies the calculations and allows us to derive the low-energy…
Spiking activity in cortical networks is nonlinear in nature. The linear-nonlinear cascade model, some versions of which are also known as point-process generalized linear model, can efficiently capture the nonlinear dynamics exhibited by…
We employ the conformal bootstrap to re-examine the problem of finding the critical behavior of four-Fermion theory at its strong coupling fixed point. Existence of a solution of the bootstrap equations indicates self-consistency of the…
The effective dynamics of the low-frequency modes is derived for the O(N) symmetric scalar field theory in the broken symmetry phase. The effect of the high-frequency fluctuations is taken into account at one-loop level exactly. A new…
We use the functional renormalization group equation for the effective average action to study the fixed point structure of gravity-fermion systems on a curved background spacetime. We approximate the effective average action by the…
We introduce and solve a model of fermions hopping between neighbouring sites on a line with random Brownian amplitudes and open boundary conditions driving the system out of equilibrium. The average dynamics reduces to that of the…
Employing the Schwinger-Keldysh formalism, we formulate an effective field theory for s-wave superconducting phase transition, where the dynamical variables consist of electromagnetic gauge field and complex scalar order parameter.…
The theory of causal fermion systems is a new physical theory which aims to describe a fundamental level of physical reality. Its mathematical core is the causal action principle. In this thesis, we develop a formalism which connects the…
New techniques for evaluating the closed time path action for non-equilibrium quantum fields are presented. A derivative expansion is performed using a proper time kernel. Applications relevant to the scalar field theory of warm inflation…