scholarly journals The Planar Thirring Model with Kähler-Dirac Fermions

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1523
Author(s):  
Simon Hands
Keyword(s):  
Degrees Of Freedom ◽  
Differential Forms ◽  
Continuum Theory ◽  
Geometric Approach ◽  
Mass Term ◽  
Thirring Model ◽  
Dirac Fermions ◽  
Long Wavelength ◽  
Fermion Fields ◽  
Lattice Fermions

Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)⊗U(N) field transformations and has a parity-invariant mass term, which are symmetries shared in common with staggered lattice fermions. The formalism is used to construct a version of the Thirring model with contact interactions between conserved Noether currents. Under reasonable assumptions about field rescaling after quantum corrections, a more general interaction term is derived, sharing the same symmetries but now including terms which entangle spin and taste degrees of freedom, which exactly coincides with the leading terms in the staggered lattice Thirring model in the long-wavelength limit. Finally, truncated versions of the theory are explored; it is found that excluding scalar and pseudoscalar components leads to a theory of six-component fermion fields describing particles with spin 1, with fermion and antifermion corresponding to states with definite circular polarisation. In the UV limit, only transverse states with just four non-vanishing components propagate. Implications for the description of dynamics at a strongly interacting renormalisation group fixed point are discussed.

ON BOSE-FERMI EQUIVALENCE IN A U(1) GAUGE THEORY WITH CHERN-SIMONS ACTION

1990 ◽  
Vol 05 (08) ◽  
pp. 593-603 ◽  
Author(s):  
N. SHAJI ◽  
R. SHANKAR ◽  
M. SIVAKUMAR
Keyword(s):  
Dirac Fermion ◽  
Complex Scalar ◽  
Abelian Gauge ◽  
Long Wavelength ◽  
Integral Methods ◽  
Fermion Fields ◽  
Long Wavelength Approximation ◽  
Complex Scalar Field ◽  
Wavelength Approximation ◽  
Chern Simons

We show, using path integral methods, that a complex scalar field in 2+1 dimensions coupled to an abelian gauge field with Chern-Simons action is equivalent to a free Dirac fermion. We show the equivalence of the vacuum functional and construct the fermion fields explicitly. Our proof is independent of the long wavelength approximation.

scholarly journals The ABC of Higher-Spin AdS/CFT

Universe ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 18 ◽  
Author(s):  
Simone Giombi ◽  
Igor Klebanov ◽  
Zhong Tan
Keyword(s):  
Free Field ◽  
Dirac Fermions ◽  
Coupling Constant ◽  
Type B ◽  
Free Energies ◽  
Fermion Fields ◽  
Higher Spin ◽  
Fermionic Fields ◽  
Type C ◽  
Type Ab

In recent literature, one-loop tests of the higher-spin AdS d + 1 /CFT d correspondences were carried out. Here, we extend these results to a more general set of theories in d > 2 . First, we consider the Type B higher spin theories, which have been conjectured to be dual to CFTs consisting of the singlet sector of N free fermion fields. In addition to the case of N Dirac fermions, we carefully study the projections to Weyl, Majorana, symplectic and Majorana–Weyl fermions in the dimensions where they exist. Second, we explore theories involving elements of both Type A and Type B theories, which we call Type AB. Their spectrum includes fields of every half-integer spin, and they are expected to be related to the U ( N ) / O ( N ) singlet sector of the CFT of N free complex/real scalar and fermionic fields. Finally, we explore the Type C theories, which have been conjectured to be dual to the CFTs of p-form gauge fields, where p = d 2 − 1 . In most cases, we find that the free energies at O ( N 0 ) either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT. Interpreting these non-vanishing values as shifts of the bulk coupling constant G N ∼ 1 / ( N − k ) , we find the values k = − 1 , − 1 / 2 , 0 , 1 / 2 , 1 , 2 . Exceptions to this rule are the Type B and AB theories in odd d; for them, we find a mismatch between the bulk and boundary free energies that has a simple structure, but does not follow from a simple shift of the bulk coupling constant.

scholarly journals Relativistic currents on ideal Aharonov–Bohm cylinders

2016 ◽  
Vol 30 (26) ◽  
pp. 1650190 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Doru-Marcel S. Băltăţeanu ◽  
Ion I. Cotăescu
Keyword(s):  
Angular Momentum ◽  
Dirac Equation ◽  
Relativistic Theory ◽  
Degrees Of Freedom ◽  
Total Angular Momentum ◽  
Relativistic Effect ◽  
Dirac Fermions ◽  
Persistent Currents ◽  
Relativistic Approach ◽  
Aharonov Bohm

The relativistic theory of the Dirac fermions moving on cylinders in external Aharonov–Bohm (AB) field is built starting with a suitably restricted Dirac equation whose spin degrees of freedom are not affected. The exact solutions of this equation on finite or infinite AB cylinders allow one to derive the relativistic circular and longitudinal currents pointing out their principal features. It is shown that all the circular currents are related to the energy in the same manner on cylinders or rings either in the relativistic approach or in the nonrelativistic one. The specific relativistic effect is the saturation of the circular currents for high values of the total angular momentum. Based on this property some approximative closed formulas are deduced for the total persistent current at [Formula: see text] on finite AB cylinders. Moreover, it is shown that all the persistent currents on finite cylinders or rings have similar nonrelativistic limits.

scholarly journals Quantum Holography from Fermion Fields

2021 ◽  
Vol 3 (3) ◽  
pp. 576-591
Author(s):  
Paola Zizzi
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Boundary Surface ◽  
Holographic Principle ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Fuzzy Sphere ◽  
Fermion Fields ◽  
Planck Unit

In this paper, we demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogolyubov transformations lead to pairs of the spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

CONTROL OF A COMPLIANT HUMANOID ROBOT IN DOUBLE SUPPORT PHASE: A GEOMETRIC APPROACH

2012 ◽  
Vol 09 (01) ◽  
pp. 1250004 ◽  
Author(s):  
GUSTAVO MEDRANO CERDA ◽  
HOUMAN DALLALI ◽  
MARTIN BROWN
Keyword(s):  
Energy Efficiency ◽  
Degrees Of Freedom ◽  
Geometric Approach ◽  
Research Problem ◽  
Bipedal Walking ◽  
Constrained Motion ◽  
Double Support ◽  
Compliant Actuators ◽  
Support Phase ◽  
Double Support Phase

Enhancing energy efficiency of bipedal walking is an important research problem that has been approached by design of recently developed compliant bipedal robots such as CoMan. While compliance leads to energy efficiency, it also complicates the walking control system due to further under-actuated degrees of freedom (DoF) associated with the compliant actuators. This problem becomes more challenging as the constrained motion of the robot in double support is considered. In this paper this problem is approached from a multi-variable geometric control aspect to systematically account for the compliant actuators dynamics and constrained motion of the robot in double support phase using a detailed electro-mechanical model of CoMan. It is shown that the formulation of constraint subspace is non-trivial in the case of non-rigid robots. A step-wise numerical algorithm is provided and the effectiveness of the proposed method is illustrated via simulation, using a ten DoF model of CoMan.

ASYMPTOTIC BEHAVIOUR OF THE VACUUM ENERGY FOR SMALL SKYRMIONS

1990 ◽  
Vol 05 (18) ◽  
pp. 3549-3597 ◽  
Author(s):  
JOSEF A. ZUK
Keyword(s):  
Field Theory ◽  
Asymptotic Behaviour ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Functional Dependence ◽  
Analytical Approximation ◽  
Low Energy ◽  
Fermion Fields ◽  
Self Consistent ◽  
Vacuum Instability

Various schemes for deriving effective Lagrangians, involving both quark and meson degrees of freedom, which are intermediate between QCD and low-energy pion dynamics have been proposed. While integration over the fermion fields within the framework of renormalized field theory leads to a vacuum instability, physically reasonable results are obtained for the theory taken with finite cut-off. In principle, properties of the nucleon, such as its mass, can be obtained from a self-consistent calculation in the Skyrmion sector. This procedure can be simplified by implementing an analytical approximation for the fermion vacuum energy which plays a central role. We discuss such an approximation, and use it to calculate exactly the asymptotic behaviour of the vacuum energy for small Skyrmions. It is found that, unlike in the renormalized theory, its functional dependence on the Skymion radius in this limit depends on the characteristics of the Skyrmion profile and choice of regularization scheme; however, the cut-off field theory exhibits no vacuum instability.

scholarly journals Gravity and quantum theory: Domains of conflict and contact

2019 ◽  
Vol 29 (01) ◽  
pp. 2030001
Author(s):  
T. Padmanabhan
Keyword(s):  
Thermal Properties ◽  
Cosmological Constant ◽  
First Principles ◽  
Degrees Of Freedom ◽  
Dynamical Variable ◽  
Quantum Structure ◽  
Cosmological Constant Problem ◽  
Metric Tensor ◽  
Long Wavelength ◽  
Thermodynamic Interpretation

There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer-dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength limit should be described in thermodynamic language and not in a geometric language. Second clue is related to the existence of the cosmological constant. Its understanding from first-principles will require the dynamical principles of the theory to be invariant under the shift [Formula: see text]. This puts strong constraints on the nature of gravitational dynamics and excludes metric tensor as a fundamental dynamical variable. In fact, these two clues are closely related to each other. When the dynamical principles are recast, respecting the symmetry [Formula: see text], they automatically acquire a thermodynamic interpretation related to the first clue. The first part of this review provides a pedagogical introduction to thermal properties of the horizons, including some novel derivations. The second part describes some aspects of cosmological constant problem and the last part provides a perspective on gravity which takes into account these principles.

scholarly journals On the Higgs mass fine-tuning problem with multi-Higgs doublet models

2019 ◽  
Vol 34 (05) ◽  
pp. 1950025 ◽  
Author(s):  
Nabarun Chakrabarty ◽  
Indrani Chakraborty
Keyword(s):  
Large Hadron Collider ◽  
Degrees Of Freedom ◽  
Higgs Mass ◽  
Hadron Collider ◽  
Mass Term ◽  
Higgs Doublet ◽  
Fine Tuning ◽  
Divergent Term ◽  
Dimensional Models ◽  
Manageable Level

With no conclusive signal till date of the minimal supersymmetric and extra-dimensional models at the Large Hadron Collider (LHC), the issue of naturalness of the Higgs mass still calls for attention. One way to achieve that is to introduce additional bosonic degrees of freedom and rely on fine-tuning thereafter. That is, to arrange for a cancellation between various parameters so that the coefficient of the quadratically divergent term in the Higgs mass is vanishing or small to a manageable level. In this work, we explore the possibility of doing so using two- and three-Higgs doublet models. We consider different versions of the same and fold in various relevant constraints accordingly. The study reveals that the quadratically divergent mass term of the 125 GeV Higgs can be exactly canceled in most of the models considered here. However, the same does not hold for the nonstandard scalars owing to the applied constraints.

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