相关论文: Quartic Anharmonicity in Different Spatial Dimensi…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
In this paper, we consider the resummation of the divergent Rayleigh-Shrodinger perturbation expansion for the ground state energy of the quartic anharmonic oscillator in one dimension. We apply the Borel-Pade resummation method combined…
The apparent breakdown of unitarity in low order perturbation theory is often is used to place bounds on the parameters of a theory. In this work we give an algorithm for approximately computing the next-to-leading order (NLO)…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
Solving quantum field theories at strong coupling remains a challenging task. The main issue is that the usual perturbative series are asymptotic series which can be useful at weak coupling but break down completely at strong coupling. In…
The process of equilibration in phi^4 theory is investigated for a homogeneous system in 3+1 dimensions and a variety of out-of-equilibrium initial conditions, both in the symmetric and broken phase, by means of the 2PI effective action.…
Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms,…
Perturbation theory and renormalization group methods are used to derive a finite-size scaling theory for the partition function zeroes and thermodynamic functions in the $O(n)$ $\phi^4$ model in four dimensions. The leading power--law…
We describe the generalization of spherical field theory to other modal expansion methods. The main approach remains the same, to reduce a d-dimensional field theory into a set of coupled one-dimensional systems. The method we discuss here…
For massless $\phi^4$ theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the…
We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this…
The chiral symmetry breaking in the 4-dimensional QED with the chirally invariant four-fermion interaction is discussed by using a novel path integral expression in terms of the field-strength tensor. In the local potential approximation,…
The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of…
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
With the help of variational perturbation theory we continue the renormalization constants $\phi^4$-theories in $4- \epsilon$ dimensions to strong bare couplings $g_0$ and find their power behavior in $g_0$, thereby determining all critical…
We study the noncommutative $\phi^4$ theory with spontaneously broken global O(2) symmetry in 4 dimensions. We demonstrate the renormalizability at one loop. This does not require any choice of ordering of the fields in the interaction…
The spectral problem for O(D) symmetric polynomial potentials allows for a partial algebraic solution after analytical continuation to negative even dimensions D. This fact is closely related to the disappearance of the factorial growth of…