AFRICA AND ASIA: <i>Kota Texts</i>. M. B. EMENEAU

Bender, Ernest

doi:10.1525/aa.1945.47.4.02a00140

Cited by 4 publications

(9 citation statements)

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“…The force of the potential (18) is a super long-range force and will play a dominate role in a very large cosmic scale. The gauge field theory based on the taiji gauge invariant Lagrangian (11) suggests that the accelerated cosmic expansion could be understood in terms of the cosmic force produced by the taiji gauge field in (12).…”

Section: Linear Potentials Between Baryon Galaxiesmentioning

confidence: 99%

“…For decades, it has been thought that higher-order field equations involve ghost states with non-definite energy or non-positive norm, which will upset unitarity of the theory. However, it was shown recently that this is not necessarily so, [10,11,12] and thereby one could apply fourth-order field equations to discuss physical phenomena. Bender and Mannheim proved a no-ghost theorem [10] for the fourth-order derivative Pais-Uhlenbeck oscillator model.…”

Section: Introductionmentioning

confidence: 99%

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A generalization of gauge symmetry, fourth-order gauge field equations and accelerated cosmic expansion

Hsu

2014

Mod. Phys. Lett. A

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A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new U1 gauge symmetry is repulsive among baryons. Such a constant force based on baryon charge conservation gives a field-theoretic understanding of the accelerated cosmic-expansion in the observable portion of the universe dominated by baryon galaxies. In consistent with all conservation laws and known forces, a simple rotating 'dumbbell model' of the universe is briefly discussed.

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Section: Linear Potentials Between Baryon Galaxiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A generalization of gauge symmetry, fourth-order gauge field equations and accelerated cosmic expansion

Hsu

2014

Mod. Phys. Lett. A

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“…This calculation makes use of the fact that the non-Hermiticity effects in this model diminish for energy states with larger spectral label N. More specifically it is ζ/N 2 that plays the role of the perturbation parameter. More recently, Bender and Tan [12] performed a more conventional perturbative calculation of a metric operator taking ζ as the perturbation parameter. This is the metric operator η + that is associated with the CPT -inner product (·, ·) CPT , [26].…”

Section: Series Expansion For η(X Y)mentioning

confidence: 99%

“…Expressing η + in its exponential form, η + = e −Q , and noting that Bender and Tan set = 2m = L/π = 1, take ǫ = −ζ for the coupling constant, and use "ε(x)" for " sign(x)", we can summarize their principal result (Eq. (11) of [12]) as…”

Section: Series Expansion For η(X Y)mentioning

confidence: 99%

“…These signify the arbitrariness in the choice of the (pseudo-)metric operator. Our approach allows a more direct way of addressing some of the basic practical problems arising in the application of quasi-and pseudo-Hermitian quantum mechanics, [1,3,4,5,6,7,8,9,10,12,13]. In particular it provides an extremely powerful technical tool for the perturbative calculation of the (pseudo-)metric operators for various toy models.…”

Section: Introductionmentioning

confidence: 99%

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Differential realization of pseudo-Hermiticity: A quantum mechanical analog of Einstein’s field equation

Mostafazadeh

2006

Journal of Mathematical Physics

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For a given pseudo-Hermitian Hamiltonian of the standard form: H = p 2 /2m + v(x), we reduce the problem of finding the most general (pseudo-)metric operator η satisfying H † = ηHη −1 to the solution of a differential equation. If the configuration space is R, this is a Klein-Gordon equation with a nonconstant mass term. We obtain a general series solution of this equation that involves a pair of arbitrary functions. These characterize the arbitrariness in the choice of η. We apply our general results to calculate η for the PT -symmetric square well, an imaginary scattering potential, and a class of imaginary delta-function potentials. For the first two systems, our method reproduces the known results in a straightforward and extremely efficient manner. For all these systems we obtain the most general η up to second order terms in the coupling constants. PACS number: 03.65.-w Consider a physical system described by a separable Hilbert space H and a pseudo-Hermitian Hamiltonian operator H : H → H. Let M denote the set of all linear invertible Hermitian operators η : H → H, then by definition [14] the pseudo-Hermiticity of H means that M H := {η ∈ M|H † = η Hη −1 } is a nonempty subset of M. The elements of M are called pseudometric operators, for they may be used to define a pseudo-inner product (a nondegenerate sesquilinear form [15]) ·|· η := ·|η· on H, where ·|· denotes the defining inner product of 1 The same way Einstein's equation does not generally restrict the metric tensor to have a particular signature, the above-mentioned equation does not restrict its solutions to correspond to positive-definite metric operators.

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Colors for textiles—Ancient and modern.

Bender¹

1947

J. Chem. Educ.

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AFRICA AND ASIA: Kota Texts. M. B. EMENEAU

Cited by 4 publications

References 0 publications

A generalization of gauge symmetry, fourth-order gauge field equations and accelerated cosmic expansion

A generalization of gauge symmetry, fourth-order gauge field equations and accelerated cosmic expansion

Differential realization of pseudo-Hermiticity: A quantum mechanical analog of Einstein’s field equation

Colors for textiles—Ancient and modern.

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