Boson Fermion Research Articles

Relativistic Fermion and Boson Fields: Bose-Einstein Condensate as a Time Crystal

In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group set is isomorphic to the SU(2) group. Such a matrix basis introduces extra six degrees of freedom of matter motion in space-time. There are three rotations about three space axes and three boosts along these axes. Next one declares the differential generating operators acting on the energy-momentum density tensor written in the above quaternion basis. The subsequent actions of this operator together with its transposed one on the above tensor lead to the emergence of the gravitomagnetic equations that are like the Maxwell equations. Wave equations extracted from the gravitomagnetic ones describe the propagation of energy density waves and their vortices through space. The Dirac equations and their reduction to two equations with real-valued functions, the quantum Hamilton-Jacobi equations and the continuity equations, are considered. The Klein-Gordon equations arising on the mass shell hints to the alternation of the paired fermion fields and boson ones. As an example, a Feynman diagram of an electron–positron time crystal is illustrated.

Unavoidable Higgs coupling deviations in the Z2 -symmetric Georgi-Machacek model

The $Z_{2}$-symmetric version of the Georgi-Machacek model does not possess a decoupling limit in which all the new particles can be made arbitrarily heavy, opening the possibility that the model can be entirely excluded if experiments reveal no deviations from the Standard Model. We explore this model, focusing on the part of parameter space in which the vacuum expectation value of the triplets, $\nu_\chi$, is small. In the small-$\nu_\chi$ limit, the second custodial-singlet scalar field $S$ necessarily becomes very light and can contribute to the total width of the 125 GeV Higgs boson $h$ via $h \to SS$. We show that this process, together with LHC measurements of the $h \to \gamma\gamma$ rate, entirely excludes masses $m_S < m_h/2$ and thereby severely constrains the parameter space, setting an experimental lower bound $\nu_\chi \gtrsim 12.5$ GeV on the vacuum expectation value of the triplets. This lower bound makes it impossible to avoid deviations from the Standard Model in the couplings of $h$ to fermion and vector boson pairs. We study the remaining parameter space after imposing constraints from direct searches for the additional Higgs bosons, and show that it is on the edge of being fully excluded at $95\%$ confidence level by LHC measurements of the 125 GeV Higgs boson's couplings. Measurements of these couplings at the future high-luminosity run of the LHC will have sufficient precision to entirely exclude the model at $5\sigma$ if no deviations from the Standard Model are observed.

Transfer reactions between odd-odd and even-even nuclei by using the interacting boson fermion fermion model and 0νββ decay in closure approximation

Spectroscopic amplitudes (SAs) in the interacting boson fermion fermion model (IBFFM) are necessary for the computation of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay but also for cross sections of heavy-ion reactions, in particular, double charge exchange reactions for the NUMEN Collaboration, if one does not want to use the closure limit. We present for the first time (i) the formalism and operators to compute in a general case the spectroscopic amplitudes in the IBFFM scheme from even-even to odd-odd nuclei, in a way suited to be used in reaction code, i.e., extracting the contribution of each orbital; (2) the odd-odd nuclei as described by the old IBFFM are obtained for the first time with the new implementation of machine learning (ML) techniques for fitting the parameters, getting a more realistic description. The one-body transition densities for $^{116}\mathrm{Cd}\ensuremath{\rightarrow}^{116}\mathrm{In}$ and $^{116}\mathrm{In}\ensuremath{\rightarrow}^{116}\mathrm{Sn}$ are part of the experimental program of the NUMEN experiment, which aims to find constraints on $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay matrix elements. As a first application of the spectroscopic amplitudes we present the calculation of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ nuclear matrix elements in the IBFFM formalism in closure approximation.

The massless thermal field and the thermal fermion bosonization in two dimensions

We come back to the issue of bosonization of fermions in two spacetime dimension and give a new costruction in the steady state case where left and right moving particles can coexist at two different temperatures. A crucial role in our construction is played by translation invariant infrared states and the corresponding field operators which are naturally linked to the infrared behaviour of the correlation functions. We present two applications: a simple new derivation in the free relativistic case of a formula by Bernard and Doyon and a full operator solution of the massless Thirring model in the steady state case where the left and right movers have two distinct temperatures.

A Boson–Fermion theory that goes beyond the BCS approximations for superconductors

A detailed analysis is given of the effects of common and recurring approximations used in conventional superconductivity theories on the condensation energy values, whose magnitudes are notoriously smaller than those of other energies as the superconducting energy gap and the chemical potential. These approximations come from using the density of states N(ɛ) and the chemical potential μ(T) either constant or temperature-dependent, respectively. We use these approximations, a total of three, to calculate the critical temperature Tc, the superconductor energy gap Δ(T), the chemical potential μ(T) and the thermodynamic potential Ω(T) which are needed to obtain the condensation energy, and compare them with the exact case, i.e., where no approximations are used. To do this, we use a ternary Boson–Fermion theory of superconductivity composed of unbound electrons (or holes) as fermions plus two-electron and two-hole Cooper pairs, both as bosons. Although all these approximations lead to reasonable values of Tc and Δ(T), the resulting thermodynamic and chemical potentials are quite different, so that the condensation energy value could be incorrect. However, when N(ɛ) and μ(T) variables are used, together with a correct physical interpretation of the condensation energy as the sum of the thermodynamic and chemical potential differences, it leads to a better agreement with reported experimental data, compared to the one obtained when taking them as constants, particularly so for low temperatures.

A radiatively induced inverse seesaw model with hidden U(1) gauge symmetry

We propose an inverse seesaw scenario under hidden U(1) gauge symmetry, having rather natural hierarchies among neutral fermion mass scales. The hierarchies are derived from theory and experimental constraints. The theory requires Majorana exotic masses have to be induced at one-loop level. The experimental side requests that the Dirac mass terms has to be highly suppressed to satisfy the constraints from the lepton flavor violations (LFVs) such as mu rightarrow egamma . In order to induce such a small Majorana exotic masses we introduce exotic fermions and bosons that also provide us additional intriguing phenomenologies such as muon anomalous magnetic moment, dark matter candidate as well as LFVs and deviations in leptonic Z decays. We analyze these phenomenologies including neutrino oscillation data numerically, and show allowed region. Finally, we discuss the DM candidate in both the cases of fermion and scalar boson, where we focus on rather lighter range that is equal or less than 10 GeV. The dominant contributions originate from interactions of hidden gauge sector, and we show allowed ranges for both cases.

The Hilbert space of large N Chern-Simons matter theories

We demonstrate that the known expressions for the thermal partition function of large N Chern-Simons matter theories admit a simple Hilbert space interpretation as the partition function of an associated ungauged large N matter theory with one additional condition: the Fock space of this associated theory is projected down to the subspace of its quantum singlets i.e. singlets under the Gauss law for Chern-Simons gauge theory. Via the Chern-Simons / WZW correspondence, the space of quantum singlets are equivalent to the space of WZW conformal blocks. One step in our demonstration involves recasting the Verlinde formula for the dimension of the space of conformal blocks in SU(N)k and U(N)k,k′ WZW theories into a simple and physically transparent form, which we also rederive by evaluating the partition function and superconformal index of pure Chern-Simons theory in the presence of Wilson lines. A particular consequence of the projection of the Fock space of Chern-Simons matter theories to quantum (or WZW) singlets is the ‘Bosonic Exclusion Principle’: the number of bosons occupying any single particle state is bounded above by the Chern-Simons level. The quantum singlet condition (unlike its Yang-Mills Gauss Law counterpart) has a nontrivial impact on thermodynamics even in the infinite volume limit. In this limit the projected Fock space partition function reduces to a product of partition functions, one for each single particle state. These single particle state partition functions are q-deformations of their free boson and free fermion counterparts and interpolate between these two special cases. We also propose a formula for the large N partition function that is valid for arbitrary finite volume of the spatial S2 and not only at large volume.

Nonlocal correlation effects in fermionic many-body systems: Overcoming the noncausality problem

Motivated by the intriguing physics of quasi-two-dimensional fermionic systems, such as high-temperature superconducting oxides, layered transition metal chalcogenides, or surface or interface systems, the development of many-body computational methods geared at including both local and nonlocal electronic correlations has become a rapidly evolving field. It has been realized, however, that the success of such methods can be hampered by the emergence of noncausal features in the effective or observable quantities involved. Here, we present an approach wherein local many-body techniques such as dynamical mean-field theory (DMFT) are extended to nonlocal correlations and interactions, which preserves causality and has a physically intuitive interpretation. Our strategy has implications for the general class of DMFT-inspired many-body methods and can be adapted to cluster, dual boson, or dual fermion techniques with minimal effort.

Chemical potential influence on the condensation energy from a Boson–Fermion model of superconductivity

Influence of the temperature dependent chemical potential on the condensation energy from a ternary Boson–Fermion model of superconductivity is reported, it consist of unbound electrons/holes which are fermions plus two-electron and two-hole Cooper pairs which are bosons. When solving simultaneously the set of equations of the mixture (two gap-like equations, one for electron pairs and another one for hole pairs, plus the particle number conservation equation) within the weak-coupling (BCS regime), the resulting superconducting chemical potential shows a shift from its normal state counterpart, which is related to both the magnitude of the temperature-dependent superconducting gap and to the Fermi energy of the superconductor. As predicted by van der Marel in the early 1990s we also find that the superconducting chemical potential has a prominent kink at critical temperature Tc, which in turn coincides with the normal state chemical potential. Also there is a discontinuity in its first derivative which directly affects the magnitude in the specific heat jump. We show that the difference between the superconducting and normal state chemical potentials is of the same order of magnitude as the corresponding difference between the thermodynamic potentials for the mixture, and must therefore be accounted for in the condensation energy calculations instead of ignoring it as is done often. The condensation energy obtained here shows very good agreement with experimental data for elemental superconductors.

Investigation of Structure and Nuclear Shape Phase Transition in Odd Nuclei in a multi-j model

In this paper‎, ‎we study the nature of the dynamics in second-order Quantum Phase Transition (QPT) between vibrational ( ) and -unstable ( ) nuclear shapes‎. ‎Using a transitional Hamiltonian according to an affine SU(1,1) algebra in combination with a coherent state formalism, Shape Phase Transitions (SPT) in odd-nuclei in the framework of the Interacting Boson Fermion Model (IBFM) are investigated‎. ‎Classical analysis reveals a change in the system along with the transition in a critical point‎. ‎The role of a fermion with angular momentum j at the critical point on quantum phase transitions in bosonic systems is investigated via a semi-classical approach‎. ‎The effect of the coupling of the odd particle to an even-even boson core is discussed along with the shape transition and‎, ‎in particular‎, ‎at the critical point‎. Our study confirms the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and determine the critical point's precise position‎.

Spin-Dependent Scattering of Scalar and Vector Dark Matter on the Electron

The property of dark matter remains to date unknown. However, a model-independent classification of dark matter candidates can be achieved by using various symmetries, as performed in the standard model. Fermionic dark matter has been extensively researched, and one favored candidate is the neutralino in the Minimal Supersymmetric Standard Model, which is required by fermion–boson symmetry and the preservation of R-parity. Bosonic dark matter has not been sufficiently studied, especially the scenario of dark matter with a mass of sub-GeV. In this paper, we consider the effect of spin-dependent (SD) on scalar and vector dark matter, which are mediated by pseudoscalar and axial-vector, and evaluate the effect on the dark matter–electron scattering cross-section. We list all the interactions and form factor of dark matter–electron SD scattering, and use XENON10/100/1T experiment data to derive the exclusion limit of the SD cross-section. We find that the SD scattering of scalar and vector dark matter can be three orders of magnitude stronger than spin-independent (SI) scattering due to the p-wave scattering.

Scaling of the finite-size effect of the α -Rényi entropy in disjointed intervals under dilation

The $\alpha$-R\'enyi entropy in the gapless models have been obtained by the conformal field theory, which is exact in the thermodynamic limit. However, the calculation of its finite size effect (FSE) is challenging. So far only the FSE in a single interval in the XX model has been understood and the FSE in the other models and in the other conditions are totally unknown. Here we report the FSE of this entropy in disjointed intervals $A = \cup_i A_i$ under a uniform dilation $\lambda A$ in the XY model, showing of a universal scaling law as \begin{equation*} \Delta_{\lambda A}^\alpha = \Delta_A^\alpha \lambda^{-\eta} \mathcal{B}(A, \lambda), \end{equation*} where $|\mathcal{B}(A, \lambda)| \le 1$ is a bounded function and $\eta = \text{min}(2, 2/\alpha)$ when $\alpha < 10$. We verify this relation in the phase boundaries of the XY model, in which the different central charges correspond to the physics of free Fermion and free Boson models. We find that in the disjointed intervals, two FSEs, termed as extrinsic FSE and intrinsic FSE, are required to fully account for the FSE of the entropy. Physically, we find that only the edge modes of the correlation matrix localized at the open ends $\partial A$ have contribution to the total entropy and its FSE. Our results provide some incisive insight into the entanglement entropy in the many-body systems.

Electron Number Density and Coherence Length of Boson-Fermion Pair in HTSC

A Bose-Einstein Condensate (BEC) of a nonzero momentum Cooper pair constitutes a composite boson or simply a boson. Previously, it has been shown that the quantum coherence of the two-component BEC (boson and fermion condensates) is controlled by plasmons where &lt; 1 % of plasmon energy mediates the charge pairing but most of the plasmon energy is used to overcome the modes that compete against superconductivity such as phonons, charge density waves, antiferromagnetism, and damping effects. The dependence of plasmon frequency on the material of a superconductor reveals that modes within a specific range of frequency enhance superconductivity and therefore affect the critical temperature of a particular superconducting material. Against this background, we study the effect on doping on boson-fermion pairing energy and hence the critical temperature. While most hole doping agents are atoms lighter than copper, many of the electron doping agents are materials heavier than copper. This property defines the doping effect on the plasma frequency. Heavier dopants lower the critical temperature while lighter dopants increase the critical temperature of a superconductor. The number density of electrons is also found to be proportional to the square of critical temperature T c while the size of a boson-fermion pair condensate (BFPC) is proportional to T c − 2 / 3 . The size of a BFPC particle is less than boson-fermion (BF) coherence length by almost an order.

Position-space representation of charged particles\u2019 propagators in a constant magnetic field as an expansion over Landau levels

We have obtained propagators in the position space as an expansion over Landau levels for the charged scalar particle, fermion, and massive vector boson in a constant external magnetic field. The summation terms in the resulting expressions consisted of two factors, one being rotationally invariant in the 2-dimensional Euclidean space perpendicular to the direction of the field, and the other being Lorentz-invariant in the 1+1-dimensional space-time. The obtained representations are unique in the sense that they allow for the simultaneous study of the propagator from both space-time and energetic perspectives which are implicitly connected. These results contribute to the development of position-space techniques in QFT and are expected to be of use in the calculations of loop diagrams.

Super modified KP hierarchy in Kac–van de Leur construction

In this paper, the modified KP hierarchy in the Kupershmidt–Kiso version is extended to the super case by Kac–van de Leur construction, that is, using highest weight representations of the even part in the tensor product of the infinite-dimensional Lie superalgebra gl∞|∞ with Grassmann algebra G. First, the super modified KP (SmKP) hierarchy is constructed in terms of superfermionic bilinear equations. Then, the superbosonic form of the SmKP hierarchy is given by super boson–fermion correspondence. With the help of super Hirota bilinear operators, the corresponding super Hirota bilinear equations of the SmKP hierarchy are obtained. Next, the Darboux transformations of this new SmKP hierarchy are expressed in the form of free superfermions and various solutions are derived. Finally, the super bilinear equations in the form of super wave functions are also constructed from the superbosonic ones, which is hoped to be helpful to obtain the corresponding Lax structures.

Bilinear equations in Darboux transformations by Boson–Fermion correspondence

Bilinear equation is an important property for integrable nonlinear evolution equation. Many famous research objects in mathematical physics, such as Gromov–Witten invariants, can be described in terms of bilinear equations to show their connections with the integrable systems. Here in this paper, we mainly discuss the bilinear equations of the transformed tau functions under the successive applications of the Darboux transformations for the KP hierarchy, the modified KP hierarchy (Kupershmidt–Kiso version) and the BKP hierarchy, by the method of the Boson–Fermion correspondence. The Darboux transformations are considered in the Fermionic picture, by multiplying the different Fermionic fields on the tau functions. Here the Fermionic fields are corresponding to the (adjoint) eigenfunctions, whose changes under the Darboux transformations are showed to be the ones of the squared eigenfunction potentials in the Bosonic picture, used in the spectral representations of the (adjoint) eigenfunctions. Then the successive applications of the Darboux transformations are given in the Fermionic picture. Based upon this, some new bilinear equations in the Darboux chain are derived, besides the ones of (l−l′) -th modified KP hierarchy. The corresponding examples of these new bilinear equations are given.

Polynomial Tau-Functions for the Multicomponent KP Hierarchy

In a previous paper we constructed all polynomial tau-functions of the 1-component KP hierarchy, namely, we showed that any such tau-function is obtained from a Schur polynomial $s\_{\lambda}(t)$ by certain shifts of arguments. In the present paper we give a simpler proof of this result, using the (1-component) boson–fermion correspondence. Moreover, we show that this approach can be applied to the $s$-component KP hierarchy, using the $s$-component boson–fermion correspondence, finding thereby all its polynomial tau-functions. We also find all polynomial tau-functions for the reduction of the $s$-component KP hierarchy, associated to any partition consisting of $s$ positive parts.

Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound

Consistency with position space OPE limit requires three-point momentum space CFT correlators to have only total energy singularity. We show that this requirement gives a simple proof of the known result that in three dimensions the parity-odd structure cannot exist for three-point correlators of exactly conserved currents with spins si, sj, sk, when triangle inequality si ≤ sj + sk is violated. We also show that even for parity even correlation functions the properties are different inside and outside the triangle. It was previously shown that if we allow for weakly broken higher spin symmetry, parity-odd correlators can exist even when triangle inequality is violated. In this paper we establish a relation between non-conservation Ward-Takahashi (WT) identities for weakly broken currents at large N and the WT identities for exactly conserved currents with the help of a few examples. This allows us to calculate the parity violating results outside the triangle using parity-even free bosonic and free fermionic results.In general, there is one parity-odd structure and two parity-even structures for three-point functions. It can be shown that the coefficient of one of the parity-even and odd parts can be combined into a complex parameter c when correlators are expressed in spinor-helicity variables. When this complex parameter takes real value c = ±1 it corresponds to either the free boson or free fermion theory. When c is a pure phase, it corresponds to Chern-Simons matter theories. Furthermore, re-expressing known results for conformal collider bounds we see that |c| ≤ 1 for generic 3d CFTs and |c| ≤ f(∆gap) for holographic CFTs.

Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters. The boson–fermion correspondence for these symmetric functions have been presented. In virtue of quantum fields, we derive a series of infinite order nonlinear integrable equations, namely, universal character hierarchy, symplectic KP hierarchy and symplectic universal character hierarchy, respectively. In addition, the solutions of these integrable systems have been discussed.

Horndeski fermion–boson stars

We establish the existence of static and spherically symmetric fermion–boson stars, in a low energy effective model of (beyond) Horndeski theories. These stars are in equilibrium, and are composed by a mixing of scalar and fermionic matters that only interact gravitationally one with each other. Properties such as mass, radius, and compactness are studied, highlighting the existence of two families of configurations defined by the parameter c 4. These families have distinctive properties, although in certain limits both are reduced to their counterparts in general relativity (GR). Finally, by assuming the same conditions used in GR, we find the maximum compactness of these hybrid stars and determine that it remains below the so-called Buchdahl’s limit.