Quartic Self-interaction Research Articles

Self-interacting Elko dark matter with an axis of locality

This communication is a natural and nontrivial continuation of the 2005 work of Ahluwalia and Grumiller on Elko. Here we report that Elko breaks Lorentz symmetry in a rather subtle and unexpected way by containing a `hidden' preferred direction. Along this preferred direction, a quantum field based on Elko enjoys locality. In the form reported here, Elko offers a mass dimension one fermionic dark matter with a quartic self-interaction and a preferred axis of locality. The locality result crucially depends on a judicious choice of phases.

Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s=1,3/2,.. and for the lattice euclidean scalar field theory with quartic self-interaction, on the simple cubic and the body-centered cubic lattices. Our bivariate high-temperature expansions, which extend through K^24, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.

Super-Hubble de Sitter fluctuations and the dynamical RG

Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales. This growth can lead to a breakdown of perturbation theory at late times. We argue that Dynamical Renormalization Group (DRG) techniques provide a convenient framework for interpreting and resumming these secularly growing terms. In the case of a massless scalar field in de Sitter with quartic self-interaction, the resummed result is also less singular in the infrared, in precisely the manner expected if a dynamical mass is generated. We compare this improved infrared behavior with large-N expansions when applicable.

Primitively divergent diagrams in a scalar field with quartic self-interaction and a kappa-deformed dispersion relation

We obtain the dimensionally regularized primitively divergent diagrams for a scalar field model with quartic self-interaction and a kappa-deformed dispersion relation as a function of the complex dimension analytically continued to the neighborhood of all real dimensions. The result shows that the poles of those diagrams occur for odd dimensions in distinction to the poles at even dimensions of the non-deformed diagrams. Actually, the singular dimensions in the deformed case are shifted by one to the right in relation to the singular dimensions of the non-deformed case. This shifting of the poles appears as an effect of the deformation on the complex dimension plane of the dimensional regularization procedure.

Perturbative symplectic field theory and Wigner function

We study relativistic quantum field theories in phase space, based on representations of the Poincaré group, using the Moyal product. We develop a perturbative theory for quantizing fields, with functional methods in phase space. The two-point function is related to relativistic Wigner functions for bosons and fermions. As an example we analyze the complex scalar field with quartic self-interaction.

Intrinsic decoherence in the interaction of two fields with a two-level atom

We treat a relativistic quantum boson gas, described by a scalar quantum field, with quartic self-interaction (ϕ4) in three spatial dimensions: we review the known equilibrium case and present new proposals off-equilibrium. For high temperature and large spatial scales, the behaviour of the gas at equilibrium simplifies nonperturbatively (equilibrium dimensional reduction or EDR): its thermodynamics is described by classical statistical mechanics with some quantum field effects. By assumption, the initial state of the gas off-equilibrium includes interactions and inhomogeneities and is not far from thermal equilibrium. We employ real-time generating functionals and obtain the free nonequilibrium correlators at non-zero temperature. The nonequilibrium quantum gas appears to simplify nonperturbatively in the regime of high temperature and large temporal and spatial scales (nonequilibrium dimensional reduction or NEDR), its dynamics being described by classical statistical mechanics with some quantum field effects. We outline the renormalization of the ϕ4 theory, the nonequilibrium statistical mechanics of a quantum anharmonic oscillator and the high temperature simplifications, all of which provide very useful hints for NEDR in the field case. Our main proposals are NEDR and the associated new (renormalized) real-time nonequilibrium generating functionals for the ϕ4 theory.

Nonequilibrium quantum anharmonic oscillator and scalar field: high temperature approximations

We treat a relativistic quantum boson gas, described by a scalar quantum field, with quartic self-interaction (ϕ4) in three spatial dimensions: we review the known equilibrium case and present new proposals off-equilibrium. For high temperature and large spatial scales, the behaviour of the gas at equilibrium simplifies nonperturbatively (equilibrium dimensional reduction or EDR): its thermodynamics is described by classical statistical mechanics with some quantum field effects. By assumption, the initial state of the gas off-equilibrium includes interactions and inhomogeneities and is not far from thermal equilibrium. We employ real-time generating functionals and obtain the free nonequilibrium correlators at non-zero temperature. The nonequilibrium quantum gas appears to simplify nonperturbatively in the regime of high temperature and large temporal and spatial scales (nonequilibrium dimensional reduction or NEDR), its dynamics being described by classical statistical mechanics with some quantum field effects. We outline the renormalization of the ϕ4 theory, the nonequilibrium statistical mechanics of a quantum anharmonic oscillator and the high temperature simplifications, all of which provide very useful hints for NEDR in the field case. Our main proposals are NEDR and the associated new (renormalized) real-time nonequilibrium generating functionals for the ϕ4 theory.

Effect of multiple Higgs fields on the phase structure of theSU(2)-Higgs model

The $SU(2)$-Higgs model, with a single Higgs field in the fundamental representation and a quartic self-interaction, has a Higgs region and a confinement region which are analytically connected in the parameter space of the theory; these regions thus represent a single phase. The effect of multiple Higgs fields on this phase structure is examined via Monte Carlo lattice simulations. For the case of $N\ensuremath{\ge}2$ identical Higgs fields, there is no remaining analytic connection between the Higgs and confinement regions, at least when Lagrangian terms that directly couple different Higgs flavors are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for $N=2$ by introducing an asymmetry in the hopping parameters of the Higgs fields. It is found that an enhancement of the phase transitions can still occur for a moderate (10%) asymmetry in the resulting hopping parameters.

BCS-BEC crossover and phase structure of relativistic systems: A variational approach

We investigate here the BCS-BEC crossover in relativistic systems using a variational construct for the ground state and the minimization of the thermodynamic potential. This is first studied in a four-fermion point interaction model and with a BCS type ansatz for the ground state with fermion pairs. It is shown that the antiparticle degrees of freedom play an important role in the BCS-BEC crossover physics, even when the ratio of Fermi momentum to the mass of the fermion is small. We also consider the phase structure for the case of fermion pairing with imbalanced populations. Within the ansatz, thermodynamically stable gapless modes for both fermions and antifermions are seen for strong coupling in the Bose-Einstein condensation (BEC) regime. We further investigate the effect of fluctuations of the condensate field by treating it as a dynamical field and generalize the BCS ansatz to include quanta of the condensate field also in a boson-fermion model with quartic self-interaction of the condensate field. It is seen that the critical temperature decreases with inclusion of fluctuations.

CHIRAL TENSOR FIELDS AND SPONTANEOUS BREAKING OF LORENTZ SYMMETRY

Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a nonvanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.

Cosmology Is Not a Renormalization Group Flow

A critical examination is made of two simple implementations of the idea that cosmology can be viewed as a renormalization group (RG) flow. Both implementations are shown to fail when applied to a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. Cosmological evolution in this model is not driven by any RG screening of couplings but rather by inflationary particle production gradually filling an initially empty universe with a sea of long wavelength scalars.

Effective Hamiltonian for non-minimally coupled scalar fields

Performing a relativistic approximation as the generalization to a curved spacetime of the flat space Klein-Gordon equation, an effective Hamiltonian which includes non-minimial coupling between gravity and scalar field and also quartic self-interaction of scalar field term is obtained.

High‐Density Skyrmion Matter and Neutron Stars

We examine neutron star properties based on a model of dense matter composed of B=1 skyrmions immersed in a mesonic mean field background. The model realizes spontaneous chiral symmetry breaking non-linearly and incorporates scale-breaking of QCD through a dilaton VEV that also affects the mean fields. Quartic self-interactions among the vector mesons are introduced on grounds of naturalness in the corresponding effective field theory. Within a plausible range of the quartic couplings, the model generates neutron star masses and radii that are consistent with a preponderance of observational constraints, including recent ones that point to the existence of relatively massive neutron stars with mass M 1.7 Msun and radius R (12-14) km. If the existence of neutron stars with such dimensions is confirmed, matter at supra-nuclear density is stiffer than extrapolations of most microscopic models suggest.

On resumming inflationary perturbations beyond one-loop

It is well known that the correlation functions of a scalar field in a quasi-de Sitter space exhibitat the loop level cumulative infrared effects proportional to the total number of e-foldings ofinflation. Using the in–in formalism, we explore the behavior of these infrared effects in the largeN limitof an O(N)-invariant scalar field theory with quartic self-interactions. By resumming all higher-orderloop diagrams non-perturbatively, we show that the connected four-point correlationfunction, which is a signal of non-Gaussianity, is non-perturbatively enhanced with respectto its tree-level value.

Quantum stability of aw<−1phase of cosmic acceleration

We consider a massless, minimally coupled scalar with a quartic self-interaction which is released in Bunch-Davies vacuum in the locally de Sitter background of an inflating universe. It was shown, in this system, that quantum effects can induce a temporary phase of superacceleration, causing a violation of the weak energy condition on cosmological scales. In this paper, we investigate the system's stability by studying the behavior of linearized perturbations in the quantum-corrected effective field equation at one- and two-loop order. We show that the amplitude of the quantum-corrected mode function is reduced in time, starting from its initial classical (Bunch-Davies) value. This implies that the linear perturbations do not grow; hence, the model is stable. The decrease in the amplitude is in agreement with the system developing a positive (growing) mass squared due to quantum processes. The induced mass, however, remains perturbatively small and does not go tachyonic. This ensures the stability.

Conformally Coupled Scalars, Instantons, and Vacuum Instability in 4D Anti-de Sitter Space

We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M theory. The holographic effective potential is exactly calculated, allowing us to study nonperturbatively the stability of AdS4 in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS4 space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.

Aharonov–Bohm effect on noncommutative plane: A coherent state approach

We formulate in a systematic manner the coherent state approach and apply it to study Aharonov–Bohm effect in the field theory context. Within this approach, we verify that the scattering amplitude is ultraviolet finite. Also, we prove that introduction of a quartic self-interaction for the scalar field allows to obtain a smooth commutative limit.

Natural little hierarchy from a partially goldstone twin Higgs

We construct a simple theory in which the fine-tuning of the standard model is significantly reduced. Radiative corrections to the quadratic part of the scalar potential are constrained to be symmetric under a global U(4) x U(4)' symmetry due to a discrete Z_2 "twin" parity, while the quartic part does not possess this symmetry. As a consequence, when the global symmetry is broken the Higgs fields emerge as light pseudo-Goldstone bosons, but with sizable quartic self-interactions. This structure allows the cutoff scale, \Lambda, to be raised to the multi-TeV region without significant fine-tuning. In the minimal version of the theory, the amount of fine-tuning is about 15% for \Lambda = 5 TeV, while it is about 30% in an extended model. This provides a solution to the little hierarchy problem. In the minimal model, the "visible" particle content is exactly that of the two Higgs doublet standard model, while the extended model also contains extra vector-like fermions with masses ~(1-2)TeV. At the LHC, our minimal model may appear exactly as the two Higgs doublet standard model, and new physics responsible for cutting off the divergences of the Higgs mass-squared parameter may not be discovered. Several possible processes that may be used to discriminate our model from the simple two Higgs doublet model are discussed for the LHC and for a linear collider.

Two-loop scalar self-mass during inflation

We work in the locally de Sitter background of an inflating universe and consider a massless, minimally coupled scalar with a quartic self-interaction. We use dimensional regularization to compute the fully renormalized scalar self-mass-squared at one- and two-loop order for a state which is released in Bunch–Davies vacuum at t = 0. Although the field strength and coupling constant renormalizations are identical to those of flat space, the geometry induces a non-zero mass renormalization. The finite part also shows a sort of growing mass that competes with the classical force in eventually turning off this system's super-acceleration.

Quantum effects can renderw<−1on cosmological scales

We report on a revision of our previous computation of the renormalized expectation value of the stress-energy tensor of a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. This model is important because it demonstrates that quantum effects can lead to violations of the weak energy condition on cosmological scales - on average, not just in fluctuations - although the effect in this particular model is far too small to be observed. The revision consists of modifying the propagator so that dimensional regularization can be used when the dimension of the renormalized theory is not four. Although the finite part of the stress-energy tensor does not change (in D=4) from our previous result, the counterterms do. We also speculate that a certain, finite and separately conserved part of the stress tensor can be subsumed into a natural correction of the initial state from free Bunch-Davies vacuum.