相关论文: Automatic derivation of fermionic many-body theori…

A new generalized Wick theorem for interacting fields in 2D conformal field theory is described. We briefly discuss its relation to the Borcherds identity and its derivation by an analytic method. Examples of the calculations of the…

In this pedagogical note I present the operator form of Wick's theorem, i.e. a procedure to bring a product of 1-particle creation and destruction operators to normal order, with respect to some reference many-body state. Both the static…

Two consistency conditions for partition functions established by Akemann and Dam-gaard in their studies of the fermionic mass dependence of the QCD partition function at low energy ({\it a la} Leutwiller-Smilga-Verbaarschot) are…

As a counterpart of the well-known generalized Wick theorem by Bais et. al. in 1988 for interacting fields in two dimensional conformal field theory, we present a new contour integral formula for the operator product expansion of a normally…

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated…

The machinery of computing vacuum expectation values of a time-ordered sequence of position operators of the simple harmonic oscillator is already well established. It rests on a Wick theorem, which enables one to decompose such a quantity…

In this work, we generalize a recursive enumerative formula for connected Feynman diagrams with two external legs. The Feynman diagrams are defined from a fermionic gas with a two-body interaction. The generalized recurrence is valid for…

Wick's theorem provides a connection between time ordered products of bosonic or fermionic fields, and their normal ordered counterparts. We consider a generic pair of operator orderings and we prove, by induction, the theorem that relates…

The algebraic formulation of Wick's theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each…

I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the recursive equation for the Green functions, and thus…

We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The…

In the first part of this thesis we study the generalization of the recent algebraic approach to classical field theory by proposing a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is…

A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented…

Optimization-based robot control strategies often rely on first-order dynamics approximation methods, as in iLQR. Using second-order approximations of the dynamics is expensive due to the costly second-order partial derivatives of the…

This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…

We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special…

We present a treatment of many-body Fermionic systems that facilitates an expression of the well-known quantities in a series expansion of the Planck's constant. The ensuing semiclassical result contains to a leading order of the response…

In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many…

In this work, we establish a direct connection between supplemented Dyck language and the signed expectation value of chains of second quantization operators relatively to the physical vacuum and relatively to a one-determinant state.…

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such…