<i>Group Theory in Physics: An Introduction</i>

Cornwell, J. F.; Buck, W.W.

doi:10.1063/1.882453

Cited by 91 publications

(165 citation statements)

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“…We build the symmetry coordinates by applying projection operators 17,18 to internal coordinates. For this purpose we choose a specific set of matrices D l ( G) for the IRREPs l of the group.…”

Section: Symmetry Coordinates and Projection Operatorsmentioning

confidence: 99%

Molecular anharmonicity: A computer-aided treatment

1999

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We present a new software package for the theoretical treatment of anharmonic vibrational spectra of nonlinear polyatomic molecules. The package, called “B&D,” computes vibrational energies starting from sets of force constants defined as potential energy derivatives. The method employed allows us to combine experimental rotation‐vibration data with any information made available from ab initio calculations. The package follows the natural procedure in which a molecular problem is solved, both in the symbolic construction of Hamiltonian operator and basis functions and in the numerical computation of the Hamiltonian matrix elements. The novelty consists in making the entire procedure fully automatic, so that the occurrence of errors is greatly reduced and the laborious process involved in deriving and implementing the Hamiltonian is dramatically simplified. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1716–1730, 1999

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Section: Symmetry Coordinates and Projection Operatorsmentioning

confidence: 99%

Molecular anharmonicity: A computer-aided treatment

1999

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“…These fields transform according to (30), (31) and to make the transformation rule explicit, we need to compute t P a , a P and m P defined in (17), (26). In order to do that, let us first notice that the action of the D 6 generator R on Bravais sites is homogeneous, while for the unit cell basis r a , r b one gets a non-homogeneous piece (see Fig.…”

Section: Electronsmentioning

confidence: 99%

“…In the nonsymmorphic case, an additional translation u P that depends on the transformation P should be added to the right hand side of eq. (2) in order to map the lattice into itself [26]. 2 In these considerations, the group O(d) should be replaced by SO(d) if the low energy dynamics is not parity invariant.…”

Section: Low Energy Symmetries and Field Theorymentioning

confidence: 99%

Low-energy electron-phonon effective action from symmetry analysis

et al. 2013

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Based on a detailed symmetry analysis, we state the general rules to build up the effective low energy field theory describing a system of electrons weakly interacting with the lattice degrees of freedom. The basic elements in our construction are what we call the "memory tensors", that keep track of the microscopic discrete symmetries into the coarse-grained action. The present approach can be applied to lattice systems in arbitrary dimensions and in a systematic way to any desired order in derivatives. We apply the method to the honeycomb lattice and re-obtain the by now wellknown effective action of Dirac fermions coupled to fictitious gauge fields. As a second example, we derive the effective action for electrons in the kagomé lattice, where our approach allows to obtain in a simple way the low energy electron-phonon coupling terms.

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“…For example, ∂ θ 1 U is an odd superfield, while ∂ θ 1 θ 2 U is an even superfield, and so on. For further details, see the book by Cornwell [17] and the reference by DeWitt [18]. The chain rule for a Grassmann-valued composite function, f (g(x)), is [18,19] …”

Section: Supersymmetric Extensionmentioning

confidence: 99%

Supersymmetric Version of the Euler System and Its Invariant Solutions

Grundland

Hariton

2013

Symmetry

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In this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivalence conjugation classes. For some of the subalgebras, the invariants have a non-standard structure. For nine selected subalgebras, we use the symmetry reduction method to find invariants, orbits and reduced systems. Through the solutions of these reduced systems, we obtain solutions of the supersymmetric Euler system. The obtained solutions include bumps, kinks, multiple wave solutions and solutions expressed in terms of arbitrary functions.

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Group Theory in Physics: An Introduction

Cited by 91 publications

References 0 publications

Molecular anharmonicity: A computer-aided treatment

Molecular anharmonicity: A computer-aided treatment

Low-energy electron-phonon effective action from symmetry analysis

Supersymmetric Version of the Euler System and Its Invariant Solutions

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