Spin nematics revisited

2002 ◽  
Vol 12 (9) ◽  
pp. 265-265
Author(s):  
V. Cvetkovic ◽  
J. Zaanen ◽  
Z. Nussinov
Keyword(s):  
Form Factor ◽  
Symmetry Breaking ◽  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Higher Dimensions ◽  
Energy Scale ◽  
Spin Systems ◽  
Heisenberg Spin ◽  
Nematic Order ◽  
Dynamical Algebra

Biquadratic spin 1 Heisenberg spin systems can be constructed exhibiting spin nematic order in higher dimensions. In terms of the original spin degrees of freedom, the spontaneous nematic symmetry breaking generates a Z2 gauge invariance. Using a generalized Holstein-Primakoff transformation for the underlying U(3) dynamical algebra, we calculate the spin dynamical form factor. Although spin is not a gauge singlet, we find form factor to be finite at finite q and $$\backslash$omega$\backslash$$, contrary to our expectations regarding the presence of a energy scale protecting the gauge invariance. This result appears to be perturbatively stable.

scholarly journals SYMMETRY PRINCIPLE PRESERVING AND INFINITY FREE REGULARIZATION AND RENORMALIZATION OF QUANTUM FIELD THEORIES AND THE MASS GAP

2003 ◽  
Vol 18 (29) ◽  
pp. 5363-5419 ◽  
Author(s):  
YUE-LIANG WU
Keyword(s):  
Symmetry Breaking ◽  
Gauge Invariance ◽  
Energy Scale ◽  
New Method ◽  
Field Theories ◽  
Parameter Method ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Mass Gap ◽  
Scaling Symmetry

Through defining irreducible loop integrals (ILI's), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILI's are obtained to maintain the generalized Ward identities of gauge invariance in non-Abelian gauge theories. The ILI's of arbitrary loop graphs can be evaluated from the corresponding Feynman loop integrals by adopting an ultraviolet (UV) divergence preserving parameter method. Overlapping UV divergences are explicitly shown to be factorizable in the ILI's and be harmless via suitable subtractions. A new regularization and renormalization method is presented in the initial space–time dimension of the theory. The procedure respects unitarity and causality. Of interest, the method leads to an infinity free renormalization and meanwhile maintains the symmetry principles of the original theory except the intrinsic mass scale caused conformal scaling symmetry breaking and the anomaly induced symmetry breaking. Tadpole graphs of Yang–Mills gauge fields are found to play an essential role for maintaining manifest gauge invariance via cancellations of quadratically divergent ILI's. Quantum field theories (QFT's) regularized through the new method are well defined and governed by a physically meaningful characteristic energy scale (CES) Mc and a physically interesting sliding energy scale (SES) μs which can run from μs ~ Mc to a dynamically generated mass gap μs = μc or to μs = 0 in the absence of mass gap and infrared (IR) problem. For Mc → ∞, the initial UV divergent properties of QFT's are recovered and well-defined. In fact, the CES Mc and SES at μs = μc play the role of UV and IR cutoff energy scales respectively. It is strongly indicated that the conformal scaling symmetry and its breaking mechanism play an important role for understanding the mass gap and quark confinement. The new method is developed to be applicable for both underlying renormalizable QFT's and effective QFT's. It also leads to a set of conjectures on mathematically interesting numbers and functional limits which may provide deep insights in mathematics.

scholarly journals ALTERNATIVE IMPLEMENTATION OF THE HIGGS BOSON

2011 ◽  
Vol 26 (07) ◽  
pp. 461-467
Author(s):  
ROBERT FOOT ◽  
ARCHIL KOBAKHIDZE
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Energy Scale ◽  
Tree Level ◽  
Radiative Corrections ◽  
Gauge Bosons ◽  
The Standard Model ◽  
Low Energies

We discuss an alternative implementation of the Higgs boson within the Standard Model which is possible if the renormalizability condition is relaxed. Namely, at energy scale Λ the Higgs boson interacts at tree-level only with matter fermions, while the full gauge invariance is still maintained. The interactions with the electroweak gauge bosons are induced at low energies through the radiative corrections. In this scenario the Higgs boson can be arbitrarily heavy, interacting with the Standard Model fields arbitrarily weakly. No violation of unitarity in the scattering of longitudinal electroweak bosons occurs, since they become unphysical degrees of freedom at energies Λ ~ TeV.

scholarly journals The statistical mechanics of near-extremal black holes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Luca V. Iliesiu ◽  
Gustavo J. Turiaci
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Partition Function ◽  
Gauge Field ◽  
Dimensional Reduction ◽  
Degrees Of Freedom ◽  
Energy Scale ◽  
Fixed Charge ◽  
Extremal Black Hole ◽  
Extremal Black Holes

Abstract An important open question in black hole thermodynamics is about the existence of a “mass gap” between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this paper, we reliably compute the partition function of Reissner-Nordström near-extremal black holes at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge does not exhibit a gap; rather, at the expected gap energy scale, we see a continuum of states. We compute the partition function in the canonical and grand canonical ensembles, keeping track of all the fields appearing through a dimensional reduction on S2 in the near-horizon region. Our calculation shows that the relevant degrees of freedom at low temperatures are those of 2d Jackiw-Teitelboim gravity coupled to the electromagnetic U(1) gauge field and to an SO(3) gauge field generated by the dimensional reduction.

scholarly journals POSITRONIUM DECAY: GAUGE INVARIANCE AND ANALYTICITY

2002 ◽  
Vol 17 (10) ◽  
pp. 1355-1398 ◽  
Author(s):  
J. PESTIEAU ◽  
C. SMITH ◽  
S. TRINE
Keyword(s):  
Wave Function ◽  
Form Factor ◽  
Binding Energy ◽  
Gauge Invariance ◽  
Dispersion Relations ◽  
Decay Rates ◽  
Effective Form ◽  
Theoretical Predictions ◽  
Positronium Decay ◽  
Analysis Of Binding Energy

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity).A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wave function are removed. Nonfactorizable amplitudes are naturally introduced. Their dynamics are described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those nonfactorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of [Formula: see text].Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.

Optical properties of complex oxides: Vanadate ladders and related inorganic nanotubes

2002 ◽  
Vol 12 (9) ◽  
pp. 355-355
Author(s):  
J. L. Musfeldt ◽  
A. B. Sushkov ◽  
J. Jegoudez ◽  
A. Revcolevschi ◽  
P. Millet ◽  
...  
Keyword(s):  
Phase Boundary ◽  
Degrees Of Freedom ◽  
Energy Scale ◽  
Coupling Constant ◽  
Field Phase ◽  
Inorganic Nanotubes ◽  
Small Coupling ◽  
Small Coupling Constant ◽  
Na Ions ◽  
T Phase

Optical spectroscopy is a sensitive probe of charge, spin, and lattice degrees of freedom. In this talk, I will detail our magneto-optical work on alpha'-NaV2O5, a prototypical ladder material, as well as the new Na2V3O7 nanotubes. Using changes in electronic structure with temperature and applied magnetic field, we have mapped out the H-T phase diagram of alpha'-NaV2O5. We find a temperature independent phase boundary at 27 T which persists above Tc (34 K), a kink in Tc(H) near 27 T, and H$\wedge $2 behavior of Tc(H) in the high field phase with an unusually small coupling constant. The energy scale of Tc and the newly discovered phase boundary at Hc (27 T) are identical. Confinement effects are investigated in the related nanotubes. Results include a larger gap than in analogous bulk materials as well as a low-energy rattling mode, which corresponds to the motion of Na+ ions inside the nanotube.

scholarly journals Optimal phase space sampling for Monte Carlo simulations of Heisenberg spin systems

2019 ◽  
Vol 31 (9) ◽  
pp. 095802 ◽  
Author(s):  
J D Alzate-Cardona ◽  
D Sabogal-Suárez ◽  
R F L Evans ◽  
E Restrepo-Parra
Keyword(s):  
Monte Carlo ◽  
Phase Space ◽  
Monte Carlo Simulations ◽  
Spin Systems ◽  
Heisenberg Spin

scholarly journals Linear energy bounds for Heisenberg spin systems

2002 ◽  
Vol 35 (31) ◽  
pp. 6545-6555 ◽  
Author(s):  
Heinz-J$uuml$rgen Schmidt
Keyword(s):  
Spin Systems ◽  
Heisenberg Spin ◽  
Energy Bounds

Asymmetric Bifurcation of Initially Curved Nanobeam

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Reduced Order ◽  
Euler Bernoulli Beam ◽  
Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

Brownian dynamics of self-regulated particles with additional degrees of freedom: Symmetry breaking and homochirality

2018 ◽  
Vol 97 (4) ◽  
Author(s):  
Debankur Bhattacharyya ◽  
Shibashis Paul ◽  
Shyamolina Ghosh ◽  
Deb Shankar Ray
Keyword(s):  
Symmetry Breaking ◽  
Brownian Dynamics ◽  
Degrees Of Freedom
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