We quantize scalar fluctuations in 1+1 dimensions above a classical background kink. The properties of the effective action for the corresponding classical field are studied with an exact functional method, alternative to exact Wilsonian renormalization, where the running parameter is a bare mass, and the regulator of the quantum theory is fixed. We extend this approach, in an appendix, to a Yukawa interaction in higher dimension.
A new approach to the quantization of the relativistic kink - model around the solitonic solution is developed on the ground of the collective coordinates method. The corresponding effective action is proved to be the action of the nonminimal $d=1+1$ point - particle with curvature. It is shown that upon canonical quantization this action yields the spectrum of kink - solution obtained firstly with the help of the WKB - quantization.
We investigate non-trivial topological structures in Discrete Light Cone Quantization (DLCQ) through the example of the broken symmetry phase of the two dimensional $ϕ^4$ theory using anti periodic boundary condition (APBC). We present evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extract the vacuum energy and kink mass and compare with classical and semi - classical results. We compare the DLCQ results for the number…
We discuss the one-loop quantum corrections to the mass M and central charge Z of supersymmetric solitons: the kink, the vortex and the monopole. Contrary to previous expectations and published results, in each of these cases there are nonvanishing quantum corrections to the mass. For the N=1 kink and the N=2 monopole a new anomaly in Z rescues BPS saturation (M=Z); for the N=2 vortex, BPS saturation is rescued for two reasons: (i) the quantum fluctuations of the Higgs field acquire a nontrivial phase due to the winding of the classical solution, and (ii) a fermionic zero mode used in the lite…
We study the properties of the topologically nontrivial doublet solution arisen in the biscalar theory with a fourth-power potential introducing an example of the spontaneous breaking of symmetry. We rule out the zero-brane (non-minimal point particle) action for this doublet as a particle with curvature. When quantizing it as the theory with higher derivatives, we calculate the quantum corrections to the mass of the doublet which could not be obtained by means of the perturbation theory.
A relativistically invariant scheme for the description of excited states in a one-kink sector is formulated. The normal oscillations of fluctuations against the background of a moving kink are determined. Zero mode of these oscillations is excluded automatically due to the properties of the integral equation describing normal oscillations. A Hamiltonian for elementary excitations is obtained reflecting the relativistic nature of the problem considered. (35 kb)
In this paper we propose a refinement of the heat kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat kernel expansion.
Many quantum field theoretical models possess non-trivial solutions which are stable for topological reasons. We construct a self-consistent example for a self-interacting scalar field--the quantum (or dressed) kink--using a two particle irreducible effective action in the Hartree approximation. This new solution includes quantum fluctuations determined self-consistently and nonperturbatively at the 1-loop resummed level and allowed to backreact on the classical mean-field profile. This dressed kink is static under the familiar Hartree equations for the time evolution of quantum fields. Becaus…
We examine whether the analysis of quantum corrections for the kink soliton carries over to the 't Hooft-Polyakov monopole. For the kink, it is central that the quantum fluctuations are eigenmodes of a Hermitian operator. For the monopole, we show the analogous operator is not Hermitian. This property raises some questions about the quantization procedure for a 't Hooft-Polyakov monopole.
In a two-dimensional toy model, motivated from five-dimensional heterotic M-theory, we study the collision of scalar field kinks with boundaries. By numerical simulation of the full two-dimensional theory, we find that the kink is always inelastically reflected with a model-independent fraction of its kinetic energy converted into radiation. We show that the reflection can be analytically understood as a fluctuation around the scalar field vacuum. This picture suggests the possibility of spontaneous emission of kinks from the boundary due to small perturbations in the bulk. We verify this pict…
One-loop corrections to kink masses in a family of (1+1)-dimensional field theoretical models with two real scalar fields are computed. A generalized DHN formula applicable to potentials with and without reflection is obtained. It is shown how half-bound states arising in the spectrum of the second order fluctuation operator for one-component topological kinks and the vacuum play a central r$\hat{\rm o}$le in the computation of the kink Casimir energy. The issue of whether or not the kink degeneracy exhibited by this family of models at the classical level survives one-loop quantum fluctuation…
The Casimir energy of quantum fluctuations about the classical kink configuration is computed numerically for a recently proposed lattice sine-Gordon model. This energy depends periodically on the kink position and is found to be approximately sinusoidal.
The path is explored between one-dimensional scattering through Dirac-$δ$ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two $δ$'s are related to the Casimir effect whereas two $δ$'s plus the first transparent P$\ddot{\rm o}$sch-Teller well arise in the context of the sine-Gordon kink fluctuations, both phenomena subjected to Dirichlet boundary conditions. One or two delta wells will be also explored in order to describe absorbent plates, even though the wells lead to non unitary Quantum Field Theories.
We consider topological defects for the $λϕ^4$ theory in (1+1) dimensions with a Lorentz-violating background. It has been shown, by M. Barreto et al. (2006) \cite{barreto2006defect}, one cannot have original effects in (the leading order of) single scalar field model. Here, we introduce a new Lorentz-violating term, next to leading order which cannot be absorbed by any redefinition of the scalar field or coordinates. Our term is the lowest order term which leads to concrete effects on the kink properties. We calculate the corrections to the kink shape and the corresponding mass. Quantization …
The fluctuations of 5D self-gravitating non-abelian kinks which arise from the breaking of the SU(5) X Z2 symmetric theory are analyzed within the context of brane-worlds. While tensor and vector sectors of these fluctuations behave like its counterparts in the standard abelian Z2 kinks, the mixing between the field excitations of the non-abelian kink and the scalar components of the metric makes the pure scalar sector of the theory very interesting. The spectrum of these scalar fluctuations, which includes gravitationally trapped massless modes on the core of the wall associated to the broken…
The q-deformed kink of the $λϕ^4-$model is obtained via the normalisable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyperbolic functions. From such a bosonic zero-mode the q-deformed potential in 1+1 dimensions is found, and we show that the q-deformed kink solution is a kink displaced away from the origin.
In this work we deal with a non-canonical scalar field in the two-dimensional spacetime. We search for a generalized model that is twin of the standard model, supporting the same defect structure with the same energy density. We also study the stability of the defect solution under small fluctuations, which is governed by a Sturm-Liouville equation, and show how to make it stable. The model is then modified and used in the five-dimensional spacetime to construct a thick brane that engenders the first order framework and preserves the twinlike behavior, under tensorial fluctuations of the metri…
We show that the anomalous contribution to the central charge of the 1+1-dimensional N=1 supersymmetric kink that is required for BPS saturation at the quantum level can be linked to an analogous term in the extra momentum operator of a 2+1-dimensional kink domain wall with spontaneous parity violation and chiral domain wall fermions. In the quantization of the domain wall, BPS saturation is preserved by nonvanishing quantum corrections to the momentum density in the extra space dimension. Dimensional reduction from 2+1 to 1+1 dimensions preserves the unbroken N=1/2 supersymmetry and turns the…
We study a scalar field model in a two dimensional space-time with a generalized $ϕ^4_G$ potential which has four minima, obtaining novel kink solutions with well defined properties although the potential is non-analytical at the origin. The model contains a control parameter $δ$ that breaks the degeneracy of the potential minima, giving rise to two different phases for the system. The $δ<0$ phases do not possess solitary wave solutions. At the transition point $δ=0$ all the potential minima are degenerate and three different kink solutions result. As the transition to the $δ>0$ phase takes pl…
We investigate new models for scalar fields in flat and curved spacetime. We note that the global reflection symmetry of the potential that identify the scalar field model does not exclude the presence of internal asymmetries that give rise to asymmetric structures. Despite the asymmetry, the new structures are linearly stable and in the braneworld scenario with an extra dimension of infinite extend, they may generate new families of asymmetric thick branes that are robust against small fluctuations in the warped geometry.
We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is analyzed. We find that, the linear spectrum can be described by a supersymmetric quantum mechanics problem, and the criteria for stable static solutions can be given analytically. We also construct a superpotential formalism for finding analytical static kink solutions. Using this formalism we first reproduce some existed solutions and then offer a new solutio…
A formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit "kink" solution of a real scalar field in AdS spacetime is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in two expansion parameters--associated with the hypersurface fluctuation length and the radius of AdS spacetime respectively. Two alternative methods are given for doing this. The results are expressed in terms of the trace of the extrinsic curvature and the intrinsic s…
We analyze the phemomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number $<N>$ is a thermal expectation value, and we compute the finite temperature fluctuations, $(ΔN)^2=<N^2>-<N>^2$. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopological, and is not a sharp observable. The fluctuations are due to the mixing of states inherent in any finite temperature expectation value. We analyze in detail two different cases in 1+1 dimensional …
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $ϕ^4$ models, we look at all possible extensions such that the kink second-order fluctuation operators are Schrödinger differential operators with Pöschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the fam…
Using stochastic quantization method we derive equations for correlators of quantum fluctuations around the classical solution in the massless phi^4 theory. The obtained equations are then solved in the lowest orders of perturbation theory, and the first correction to the free propagator of a quantum fluctuation is calculated.
In this paper, we first use semi-classical methods to study quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065]. In particular, we examine the fluctuations at quadratic order around the static kink solution using the background field method. We derive equations of motion for the fluctuations and argue that at O(theta^2) the spectrum of fluctuations remains essentially the same as that of the corresponding commutative theory. We compute the one-loop two-point functions of the sine-Gordon field and the additional scalar field present …
We present an analytic study of the finite size effects in Sine--Gordon model, based on the semiclassical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi--periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame' type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited …
We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This proper time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equ…
We investigate low-energy fluctuations in the real kink crystal phase of dense quark matter within the Nambu--Jona-Lasinio model. The modulated chiral condensate breaks both the translational symmetry and chiral symmetry spontaneously, which leads to the appearance of phonons and pions that are dominant degrees of freedom in the infrared. Using the Ginzburg-Landau expansion near the Lifshitz point, we derive elastic free energies for phonons and pions in dependence on the temperature and chemical potential. We show that the one-dimensional modulation is destroyed by thermal fluctuations of pho…
We obtain explicit formulas for the eight bosonic and eight fermionic fluctuations around the mixed-flux generalization of the Hofman-Maldacena giant magnon on AdS$_3 \times$S$^3 \times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. As a check of our results, we confirm that the semiclassical quantization of these fluctuations leads to a vanishing one-loop correction to the magnon energy, as expected from symmetry based arguments.
We apply the new quantization scheme outlined in Phys. Rev. D102 (2020) 125001 to explore the influence which quantum vacuum fluctuations of the spacetime metric exert on the universes of Quantum Einstein Gravity, which is regarded an effective theory here. The scheme promotes the principle of Background Independence to the level of the regularized precursors of a quantum field theory ("approximants") and severely constrains admissible regularization schemes. Without any tuning of parameters, we find that the zero point oscillations of linear gravitons on maximally symmetric spacetimes do not …
In this paper, we will constrain the operator ordering ambiguity of Wheeler-DeWitt equation by analyzing the quantum fluctuations in the universe. This will be done using a third quantized formalism. It is expected that the early stages of the universe are dominated by quantum fluctuations. Furthermore, it is also expected that these quantum fluctuations get suppressed with the expansion of the universe. We will show that this desired behavior of quantum fluctuations could be realized by a wide ranges of the factor ordering parameters. We will examined two different cosmological models, and ob…
In this series of lectures a method is developed to compute one-loop shifts to classical masses of kinks, multi-component kinks, and self-dual vortices. Canonical quantization is used to show that the mass shift induced by one-loop quantum fluctuations is the trace of the square root of the differential operator governing these fluctuations. Standard mathematical techniques are used to deal with some powers of pseudo-differential operators. Ultraviolet divergences are tamed by using generalized zeta function regularization methods and, then performing zero-point energy and mass renormalization…
We study the coupled equations describing fluctuations of scalars and the metric about background solutions of N=8 gauged supergravity which are dual to boundary field theories with renormalization group flow. For the case of a kink solution with a single varying scalar, we develop a procedure to decouple the equations, and we solve them in particular examples. However, difficulties occur in the calculation of correlation functions from the fluctuations, presumably because the AdS/CFT correspondence has not yet been properly implemented in the coupled scalar-gravity sector. Some new examples o…
In these Lectures a method is described to analyze the effect of quantum fluctuations on topological defect backgrounds up to the one-loop level. The method is based on the spectral heat kernel/zeta function regularization procedure, and it is first applied to various types of kinks arising in several deformed linear and non-linear sigma models with different numbers of scalar fields. In the second part, the same conceptual framework is constructed for the topological solitons of the planar semilocal Abelian Higgs model, built from a doublet of complex scalar fields and one U(1) gauge field.
Quantum field theory in a semiclassical background can be derived as an approximation to quantum gravity from a weak-coupling expansion in the inverse Planck mass. Such an expansion is studied for evolution on "nice-slices" in the spacetime describing a black hole of mass M. Arguments for a breakdown of this expansion are presented, due to significant gravitational coupling between fluctuations, which is consistent with the statement that existing calculations of information loss in black holes are not reliable. For a given fluctuation, the coupling to subsequent fluctuations becomes of order …
We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable small-scale dynamics, nonlinear versions of strings, so-called `chaotic strings' are introduced. These can be used to provide the `noise' for second quantization of ordinary strings via the Parisi- Wu approach of stochastic quantization. Extensive numerical evidence is presented that the vacuum energy of chaotic strings is minimized for the numerical values of the observed standard model parameters, i.e. in this extended approach to second quantization concrete predictions for vacu…
We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial quantization of the game (semiclassical) allows us to find a winning strategy for the second player, but it is unstable w.r.t. the classical strategy. However, in a fully quantum version of the game we find a winning strategy for the first player that is optimal: the symmetric classical situation is broken at the quantum level.
We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space-time where the average geometry is that of constant negative curvature and where the Hartle-Hawking boundary condition arises naturally.
