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We study the phase structure of a 4D complex scalar field theory with a potential V(Phi) = | Lambda^3 / Phi - Lambda Phi |^2 at zero and at finite temperature. The model is analyzed by mean field and Monte Carlo methods. At zero temperature the theory falls in the universality class of the 4D Ising model when varying Lambda. The situation is less clear-cut for variations w.r.t. Lambda at large temperatures and variations w.r.t. temperature at a given value of Lambda. We observe temperature independence of the mass of the first excitation.
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We investigate the nature of resonant tunneling in Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu, we describe quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.
The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here this is demonstrated in detail for two different models of the field-potential coupling. here is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully interacting quantum field theories; these terms are finite but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply rising smooth potential.
We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $varphi^4$ interaction. A bare mass is required for the theory to be massless at the quantum level. In perturbation theory the critical mass is ambiguous due to infrared (IR) divergences and we indeed find that at two-loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [Jackiw 1980, Appelquist 1981] that super-renormalisable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov-Chain-Monte-Carlo simulations of the lattice-regularised theory, both frequentist and Bayesian data analysis, and considerations of a corresponding effective theory we gather evidence that this is indeed the case.
In this paper the scattering between the non-topological kinks arising in a family of two-component scalar field theory models is analyzed. A winding charge is carried by these defects. As a consequence, two different classes of kink scattering processes emerge: (1) collisions between kinks that carry the same winding number and (2) scattering events between kinks with opposite winding number. The variety of scattering channels is very rich and it strongly depends on the collision velocity and the model parameter. For the first type of events, four distinct scattering channels are found: textit{kink reflection} (kinks collide and bounce back), textit{one-kink (partial) annihilation} (the two non-topological kinks collide causing the annihilation of one half of each kink and the subsequent recombination of the other two halves, giving rise to a new non-topological kink with the opposite winding charge), textit{winding flip kink reflection} (kinks collide and emerge with the opposite winding charge) and textit{total kink annihilation} (kinks collide and decay to the vacuum configuration). For the second type of events, the scattering channels comprise textit{bion formation} (kink and antikink form a long-living bound state), textit{kink-antikink passage} (kinks collide and pass each other) and textit{kink-antikink annihilation} (kink and antikink collide and decay to the vacuum configuration).
We generally investigate the scalar field model with the lagrangian $L=F(X)-V(phi)$, which we call it {it General Non-Canonical Scalar Field Model}. We find that it is a special square potential(with a negative minimum) that drives the linear field solution($phi=phi_0t$) while in K-essence model(with the lagrangian $L=-V(phi)F(X)$) the potential should be taken as an inverse square form. Hence their cosmological evolution are totally different. We further find that this linear field solutions are highly degenerate, and their cosmological evolutions are actually equivalent to the divergent model where its sound speed diverges. We also study the stability of the linear field solution. With a simple form of $F(X)=1-sqrt{1-2X}$ we indicate that our model may be considered as a unified model of dark matter and dark energy. Finally we study the case when the baryotropic index $gamma$ is constant. It shows that, unlike the K-essence, the detailed form of F(X) depends on the potential $V(phi)$. We analyze the stability of this constant $gamma_0$ solution and find that they are stable for $gamma_0leq1$. Finally we simply consider the constant c_s^2 case and get an exact solution for F(X)
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