Three approaches to classical thermal field theory

In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.     

Kauffman knot polynomials in classical abelian Chern-Simons field theory

Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant t^I(L) is constructed for a link L, where I is the abelian Chern-Simons action and t a formal constant. For oriented knotted vortex lines, t^I satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, t^I satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.     

Feynman diagrams to three loops in three-dimensional field theory

The two-point integrals contributing to the self-energy of a particle in a three-dimensional quantum field theory are calculated to two-loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to three-loop order. For almost every integral an expression in terms of elementary and dilogarithm functions is obtained. For two integrals, the master integral and the Mercedes integral, a one-dimensional integral representation is obtained with an integrand consisting only of elementary functions. The results are applied to a scalar λφ⁴ theory.     

Two-loop vertices in quantum field theory: infrared convergent scalar configurations

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different topologies and comparisons with analytical results, whenever available, are performed. An internal cross-check, based on alternative procedures, is also applied. The analysis of infrared divergent configurations, as well as the treatment of tensor integrals, will be discussed in two forthcoming papers.     

Effective potentials in the Lifshitz scalar field theory

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling z=2, and the mass and the coupling constants renormalization are performed whereas the finite counterterm is just needed for the highest order of the coupling because of the mild UV divergence. Finally, we investigate whether the critical temperature for the symmetry breaking can exist or not in this approximation.     

Classical and quantum theory of the massive spin-two field

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz–Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark–antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers J^PC=2⁻⁺$J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.     

The dirac-schwinger covariance condition in classical field theory

A straightforward derivation of the Dirac-Schwinger covariance condition is given within the framework of classical field theory. The crucial role of the energy continuity equation in the derivation is pointed out. The origin of higher order derivatives of delta function is traced to the presence of higher order derivatives of canonical coordinates and momenta in the energy density functional.     

On classical ferromagnets with a complex external field

We prove analyticity properties of correlation functions using correlation inequalities.     

非相对论弱相互作用玻色气体的有效场理论处理

采用有效场理论研究了非相对论弱相互作用玻色-爱因斯坦凝聚量子气体的一般性质.在分析了系统的不可重整化性质后,从有效拉氏量出发,计算了最低阶环路修正下拉氏量参量的运动耦合常数(running coupling constant)的形式,并且得到了相应的微分方程.研究结果表明,不同于相对论玻色气体的有效理论,对非相对论弱相互作用的玻色气体,可以移除该有效理论中的内禀能量尺度,即可令该有效理论的内禀能量尺度取无穷大值.所得的分析结果将有助于对玻色-爱因斯坦凝聚的临界性质和行为的深入研究.     

High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing

We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which – in contrast to the well known Moyal–Weyl deformation – lead to a theory with modified kinetic term, while all local potentials are unaffected by the deformation. We show that our models, in particular, include propagators with anisotropic scaling z=2$z=2$ in the ultraviolet (UV). For a Φ⁴${\Phi }^4$-theory on our noncommutative space we obtain an improved UV behaviour at the one-loop level and the absence of UV/IR-mixing and of the Landau pole.     

State space formalism of Feynman diagram theory for acousto-optic interactions:I.single-frequency case

A Feynman diagram theory for acousto—optic(AO)interactions is es-tablished,which provides a general method to calculate the scatteringamplitudes and intensities for both single-frequency and multifrequency AOinteractions.The method is based on counting the number of allowableFeynman diagrams.Some important assertions have been proved rigorously inthis paper.     

Evolution of coupled classical fields

We study the evolution of the coupled scalar and fermion fields within the classical field theory. We examine the case of N coupled fields in (1+3)-dimensional space. The general expressions for the fields distributions are obtained. The particular case of two fields in (1+1)-dimensional space is carefully studied. We obtain the expressions for the averaged fields intensities and show that in the relativistic limit they are similar to the usual transition probabilities formulae of neutrino oscillations.     

Exact scalar field cosmologies in a higher derivative theory

We obtain exact cosmological solutions of a higher derivative theory described by the Lagrangian L=R+2αR ² in the presence of interacting scalar field. The interacting scalar field potential required for a known evolution of the FRW universe in the framework of the theory is obtained using a technique different from the usual approach to solve the Einstein field equations. We follow here a technique to determine potential similar to that used by Ellis and Madsen in Einstein gravity. Some new and interesting potentials are noted in the presence of R ² term in the Einstein action for the known behaviours of the universe. These potentials in general do not obey the slow rollover approximation.     

洛仑兹破缺标量场的霍金隧穿辐射

把洛仑兹破缺的标量场方程推广到弯曲时空中,并通过Aether-like项对标量场方程进行修正,该项所产生的效应也会影响到黑洞时空视界附近处的物理效应.接着,进一步在半经典近似下得到了修正的Hamilton-Jacobi方程,然后用这一修正的Hamilton-Jacobi方程研究了史瓦西黑洞的隧穿辐射特征,并讨论了洛仑兹破缺对黑洞霍金辐射和黑洞熵的影响.结果表明,u~α=δ_t~αu~t,δ_r~αu~r形式的Aether-like项的效应可能使黑洞温度增加,而黑洞熵降低.该工作可以帮助我们更深刻地理解弯曲时空中的洛仑兹破缺效应的物理性质.     

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy, respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Abelian scalar theory at large global charge

We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global U (1) charge in an arbitrary number of dimensions. The ground state is coherently constructed by the zero modes and the appearance of a centrifugal potential is quantum mechanically verified. Using the path integral formulation we systematically analyze the quantum fluctuations around in order to derive an effective action for the Goldstone mode, which becomes perturbatively meaningful when the charge is large. In this regime we explicitly show, by computing the first few loop corrections, that the whole construction is stable against quantum effects, in the sense that any higher derivative couplings to Goldstone's tree‐level action are suppressed by appropriate powers of the large charge.     

Two problems in thermal field theory

In this talk, I review recent progress made in two areas of thermal field theory. In particular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate.     

Exact treatment of the Jaynes–Cummings model under the action of an external classical field

We consider the usual Jaynes–Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency ω₀ and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity.