International Journal of Modern Physics A

We review some recent developments in the understanding of field theories in the perturbative regime. In particular, we discuss the notions of analyticity, unitarity and locality, and therefore the singularity structure of scattering amplitudes in general interacting theories. We describe their tree-level structure and their on-shell representations, as well as the links between the tree-level structure itself and the structure of the loop amplitudes. Finally, we describe the on-shell diagrammatics recently proposed both on general grounds and in the remarkable example of planar supersymmetric theories.

It is well known that both the symplectic structure and the Poisson brackets of classical field theory can be constructed directly from the Lagrangian in a covariant way, without passing through the noncovariant canonical Hamiltonian formalism. This is true even in the presence of constraints and gauge symmetries. These constructions go under the names of the covariant phase space formalism and the Peierls bracket. We review both of them, paying more careful attention, than usual, to the precise mathematical hypotheses that they require, illustrating them in examples. Also an extensive historical overview of the development of these constructions is provided. The novel aspect of our presentation is a significant expansion and generalization of an elegant and quite recent argument by Forger and Romero showing the equivalence between the resulting symplectic and Poisson structures without passing through the canonical Hamiltonian formalism as an intermediary. We generalize it to cover theories with constraints and gauge symmetries and formulate precise sufficient conditions under which the argument holds. These conditions include a local condition on the equations of motion that we call hyperbolizability, and some global conditions of cohomological nature. The details of our presentation may shed some light on subtle questions related to the Poisson structure of gauge theories and their quantization.

In this paper, we introduce model-independent data analysis procedures for identifying inelastic WIMP-nucleus scattering as well as for reconstructing the mass and the mass splitting of inelastic WIMPs simultaneously and separately. Our simulations show that, with 𝒪(50) observed WIMP signals from one experiment, one could already distinguish the inelastic WIMP scattering scenarios from the elastic one. By combining two or more data sets with positive signals, the WIMP mass and the mass splitting could even be reconstructed with statistical uncertainties of less than a factor of two.

Equal-time correlation functions play a central role in the recent noncovariant approaches to infrared QCD in the Coulomb gauge. In this article, we explore the possibilities to derive equal-time correlation functions from a generating functional, represent them diagrammatically, and formulate nonperturbative relations similar to Dyson–Schwinger equations among them, in analogy to the covariant n-point functions. For simplicity, we set up the formalism for λϕ⁴ theory and derive explicit expressions for the equal-time 2- and 4-point functions.

The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The κ-deformed phase space with noncommutative coordinates is realized in terms of undeformed quantum phase space. There are infinitely many such realizations related by similarity transformations. For a given realization, we construct corresponding coproducts of commutative coordinates and momenta (bialgebroid structure). The κ-deformed phase space has twisted Hopf algebroid structure. General method for the construction of twist operator (satisfying cocycle and normalization condition) corresponding to deformed coalgebra structure is presented. Specially, twist for natural realization (classical basis) of κ-Minkowski space–time is presented. The cocycle condition, κ-Poincaré algebra and R-matrix are discussed. Twist operators in arbitrary realizations are constructed from the twist in the given realization using similarity transformations. Some examples are presented. The important physical applications of twists, realizations, R-matrix and Hopf algebroid structure are discussed.

We study the effects of light-cone fluctuations on the renormalized zero-point energy associated with a free massless scalar field in the presence of boundaries. In order to simulate light-cone fluctuations, we introduce a space–time dependent random coefficient in the Klein–Gordon operator. We assume that the field is defined in a domain with one confined direction. For simplicity, we choose the symmetric case of two parallel plates separated by a distance a. The correction to the renormalized vacuum energy density between the plates goes as 1/a⁸ instead of the usual 1/a⁴ dependence for the free case. In turn, we also show that light-cone fluctuations break down the vacuum pressure homogeneity between the plates.

We investigate the possibility of spatially inhomogeneous chiral and Cooper, or superconducting, pairing in the (1+1)-dimensional model by Chodos et al. [Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature T and quark number chemical potential μ. In the framework of the Fulde–Ferrel inhomogeneity ansatz for chiral and Cooper condensates, we show that if G₁>G₂, where G₁ and G₂ are the coupling constants in the quark–antiquark and diquark channels, then in the (μ, T)-phase diagram the superconducting phase is suppressed by spatially inhomogeneous chiral spiral phase with broken chiral symmetry. In contrast, in the above mentioned original Chodos et al. model, where only the opportunity for homogeneous condensates is taken into account, the superconducting phase is realized at sufficiently high values of μ at arbitrary values of G₂>0, including the interval 0<G₂<G₁.