Instant-form Hamiltonian and Becchi–Rouet–Stora–Tyutin formulations of the Nielsen–Olesen model in the broken symmetry phase

The usual instant-form (equal-time) Hamiltonian and BecchiRouetStoraTyutin formulations of the NielsenOlesen model are investigated in two-space one-time dimension in the broken (frozen) symmetry phase, where the phase ϕ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone boson. PACS No.: 11.10.Ef

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The front-form Hamiltonian and BRST formulations of the NielsenOlesen model in the broken symmetry phase

Canadian Journal of Physics ◽

10.1139/p03-048 ◽

2004 ◽

Vol 82 (7) ◽

pp. 569-583 ◽

Cited By ~ 7

Author(s):

Usha Kulshreshtha ◽

D S Kulshreshtha

Keyword(s):

Matter Field ◽

Degree Of Freedom ◽

Broken Symmetry ◽

Time Dimension ◽

Symmetry Phase ◽

Front Form ◽

Charge Degree ◽

Complex Matter ◽

Charge Degree Of Freedom

The front-form Hamiltonian and BRST formulations of the NielsenOlesen model are investigated in two-space one-time dimension in the broken (frozen) symmetry phase, where the phase ϕ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone Boson.PACS No.: 11.15.q

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Higgs potential from Weyl conformal gravity

Modern Physics Letters A ◽

10.1142/s0217732320503046 ◽

2020 ◽

Vol 35 (37) ◽

pp. 2050304

Author(s):

Ichiro Oda

Keyword(s):

Gauge Field ◽

Gravitational Interaction ◽

Goldstone Boson ◽

Matter Field ◽

Einstein Frame ◽

Jordan Frame ◽

Higgs Potential ◽

Conformal Gravity ◽

Symmetry Breakdown ◽

Complex Matter

We consider Weyl’s conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a [Formula: see text] term in moving from the Jordan frame to the Einstein frame. A massless Nambu–Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent to the corresponding theory in the Einstein frame via the BRST formalism.

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Twist engineering of the two-dimensional magnetism in double bilayer chromium triiodide homostructures

10.21203/rs.3.rs-356604/v1 ◽

2021 ◽

Author(s):

Hongchao Xie ◽

Xiangpeng Luo ◽

Gaihua Ye ◽

Zhipeng Ye ◽

Haiwen Ge ◽

...

Keyword(s):

Twist Angle ◽

Degree Of Freedom ◽

Two Dimensional ◽

Magnetic Ground State ◽

Linear Superposition ◽

Experimental Realization ◽

Spin Degree ◽

Charge Degree ◽

Ising Magnet ◽

Charge Degree Of Freedom

Abstract Twist engineering, or the alignment of two-dimensional (2D) crystalline layers with desired orientations, has led to tremendous success in modulating the charge degree of freedom in hetero- and homo-structures, in particular, in achieving novel correlated and topological electronic phases in moiré electronic crystals. However, although pioneering theoretical efforts have predicted nontrivial magnetism and magnons out of twisting 2D magnets, experimental realization of twist engineering spin degree of freedom remains elusive. Here, we leverage the archetypal 2D Ising magnet chromium triiodide (CrI3) to fabricate twisted double bilayer homostructures with tunable twist angles and demonstrate the successful twist engineering of 2D magnetism in them. Using linear and circular polarization-resolved Raman spectroscopy, we identify magneto-Raman signatures of a new magnetic ground state that is sharply distinct from those in natural bilayer (2L) and four-layer (4L) CrI3. With careful magnetic field and twist angle dependence, we reveal that, for a very small twist angle (~ 0.5 degree), this emergent magnetism can be well-approximated by a weighted linear superposition of those of 2L and 4L CI3 whereas, for a relatively large twist angle (~ 5 degree), it mostly resembles that of isolated 2L CrI3. Remarkably, at an intermediate twist angle (~ 1.1 degree), its magnetism cannot be simply inferred from the 2L and 4L cases, because it lacks sharp spin-flip transitions that are present in 2L and 4L CrI3 and features a dramatic Raman circular dichroism that is absent in natural 2L and 4L ones. Our results demonstrate the possibility of designing and controlling the spin degree of freedom in 2D magnets using twist engineering.

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Spontaneously Broken Symmetries

10.1093/oso/9780192844200.003.0014 ◽

2021 ◽

pp. 287-303

Author(s):

J. Iliopoulos ◽

T.N. Tomaras

Keyword(s):

Phase Transitions ◽

Vector Field ◽

Quantum Physics ◽

Goldstone Boson ◽

Internal Symmetry ◽

Higgs Mechanism ◽

Broken Symmetry ◽

Massive Vector ◽

Broken Symmetries ◽

Gauge Symmetries

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.

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Charge degree of freedom as a sensitive probe for fission mechanism

Journal of Radioanalytical and Nuclear Chemistry ◽

10.1007/bf02223370 ◽

1997 ◽

Vol 223 (1-2) ◽

pp. 99-119

Author(s):

A. Yokoyama ◽

H. Baba ◽

N. Takahashi ◽

M.-C. Duh ◽

T. Saito

Keyword(s):

Degree Of Freedom ◽

Charge Degree ◽

Charge Degree Of Freedom

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A CALCULATION OF THE MAGNETIC MOMENT OF THE Δ++

Modern Physics Letters A ◽

10.1142/s021773239300221x ◽

1993 ◽

Vol 08 (34) ◽

pp. 3283-3290

Author(s):

MILTON DEAN SLAUGHTER

Keyword(s):

Quark Model ◽

Magnetic Moment ◽

Broken Symmetry ◽

Flavor Symmetry ◽

Perturbative Calculation ◽

Gauge Invariant ◽

Equal Time ◽

Asymptotic Level ◽

Equal Time Commutation ◽

Static Quark

A fully relativistic, gauge-invariant, and non-perturbative calculation of the Δ++ magnetic moment, μΔ++, is made using equal-time commutation relations (ETCRs) and the dynamical concepts of asymptotic SU F(2) flavor symmetry and asymptotic level realization. Physical masses of the Δ and nucleon are used in this broken symmetry calculation. It is found that μΔ++=2.04μp, where μp is the proton magnetic moment. This result is very similar to that obtained by using SU(6) ⊗ O(3) symmetry or the static quark model.

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