Manifest Covariance in Relativistic Potential Theory

Abstract We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

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Sorption of phenols on hexadecyltrimethylammonium- modified bentonite: Application of Polanyi−Manes potential theory

Energy & Environment ◽

10.1177/0958305x20977286 ◽

2020 ◽

pp. 0958305X2097728

Author(s):

Jiyeon Choi ◽

Dong-Ik Slong ◽

Won Sik Shin

Keyword(s):

Molar Volume ◽

Potential Theory ◽

Characteristic Curve ◽

Chemical Compositions ◽

Pore Filling ◽

Sorption Data ◽

Similar Chemical ◽

Competitive Model ◽

Sorption Potential ◽

Sorption Systems

This study investigated the sorption of phenol and 4-chlorophenol (4-CP) on natural bentonite modified with hexadecyltrimethylammonium (HDTMA) cation. The Freundlich, Langmuir, Dubinin−Radushkevich (DR), Sips, and Polanyi−Dubinin−Manes (PDM) models fitted the sorption data well (R2 > 0.92). The Freundlich coefficient and the maximum sorbed amount of the Langmuir and PDM models of 4-CP were higher than phenol because of higher hydrophobicity (log Kow = 2.39 for 4-CP and 1.46 for phenol). The PDM model that includes solubility and molar volume was highly useful in predicting the sorption of phenols having widely different hydrophobicity and solubility. The characteristic curves, the plot of sorbed volume ( qv) versus the sorption potential per molar volume ( ε/ Vm) of 4-CP and phenol were distinctly different although they have similar chemical compositions. The selectivity of 4-CP (3.72) was higher than that of phenol (0.27) in binary sorption systems. The sorbed volume ( qv) in the binary sorption was remarkably reduced and the characteristic curve had wider distribution owing to competition in pore-filling. The sorption behaviors were elucidated by partitioning and pore-filling mechanisms. Among the tested binary sorption models, the modified Langmuir competitive model was the best in the prediction of the binary sorption (R2 > 0.98).

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A quantization of the electromagnetic field

Canadian Journal of Physics ◽

10.1139/p83-148 ◽

1983 ◽

Vol 61 (8) ◽

pp. 1172-1183

Author(s):

Anton Z. Capri ◽

Gebhard Grübl ◽

Randy Kobes

Keyword(s):

Hilbert Space ◽

Electromagnetic Field ◽

Gauge Invariance ◽

Free Field ◽

External Source ◽

Field Level ◽

Manifest Covariance ◽

The One ◽

Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

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