Papers by Amir Abbass Varshovi
International journal of geometric methods in modern physics, Apr 18, 2024
arXiv (Cornell University), Dec 7, 2021
A differential geometric statement of the noncommutative topological index theorem is worked out ... more A differential geometric statement of the noncommutative topological index theorem is worked out for covariant star products on noncommutative vector bundles. For start, a noncommutative manifold is considered as a product space X = Y × Z, wherein Y is a closed manifold, and Z is a flat Calabi-Yau m-fold. Also a semi-conformally flat metric is considered for X which leads to a dynamical noncommutative spacetime from the viewpoint of noncommutative gravity. Based on the Kahler form of Z the noncommutative star product is defined covariantly on vector bundles over X. This covariant star product leads to the celebrated Groenewold-Moyal product for trivial vector bundles and their flat connections, such as C ∞ (X). Hereby, the noncommutative characteristic classes are defined properly and the noncommutative Chern-Weil theory is established by considering the covariant star product and the superconnection formalism. Finally, the index of the ⋆-noncommutative version of elliptic operators is studied and the noncommutative topological index theorem is stated accordingly.
arXiv (Cornell University), Nov 27, 2020
The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontolo... more The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontological perspective based on the reality of (semi-) deterministic parallel worlds in the interpretation. It is demonstrated that with thanks to the uncertainty principle there would be no consistent way to specify the correct ontology of the Universe, hence the MWI is subject to an inherent contradiction which claims that the world where we live in is unreal.
arXiv (Cornell University), 2012
The theory of alpha_star-cohomology is studied thoroughly and it is shown that in each cohomology... more The theory of alpha_star-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translationinvariant non-commutative quantum field theory is physically equivalent to a Groenewold- Moyal non-commutative quantum field theory.
Physical review, Mar 7, 2018
In this paper, we discuss the noncommutative QED 2 in the S-matrix framework. We are interested i... more In this paper, we discuss the noncommutative QED 2 in the S-matrix framework. We are interested in perturbatively proving that the exact Schwinger mass μ 2 ¼ e 2 π does not receive noncommutative corrections to any order in loop expansion. In this sense, the S-matrix approach is useful since it allows us to work with the effective action Γ½A (interaction term) to compute the corresponding gauge field 1PI two-point function at higher orders. Furthermore, by means of α Ã-cohomology, we generalize the QED 2 S-matrix analysis in the Moyal star product to all translation-invariant star products.
arXiv (Cornell University), Dec 17, 2020
The entire geometric formulations of the BRST and the anti-BRST structures are worked out in pres... more The entire geometric formulations of the BRST and the anti-BRST structures are worked out in presence of the Nakanishi-Lautrup field. It is shown that in the general form of gauge fixing mechanisms within the Faddeev-Popov quantization approach, the anti-BRST invariance reflects thoroughly the classical symmetry of the Yang-Mills theories with respect to gauge fixing methods. The Nakanishi-Lautrup field is also defined and worked out as a geometric object. This formulation helps us to introduce two absolutely new topological invariants of quantized Yang-Mills theories, so called the Nakanishi-Lautrup invariants. The cohomological structure of the anti-BRST symmetry is also studied and the anti-BRST topological index is derived accordingly.
arXiv (Cornell University), Oct 3, 2012
The theory of α *-cohomology is studied thoroughly and it is shown that in each cohomology class ... more The theory of α *-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translationinvariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.
International Journal of Geometric Methods in Modern Physics
A differential geometric statement of the noncommutative topological index theorem is worked out ... more A differential geometric statement of the noncommutative topological index theorem is worked out for covariant star products on noncommutative vector bundles. To start, a noncommutative manifold is considered as a product space [Formula: see text], wherein [Formula: see text] is a closed manifold, and [Formula: see text] is a flat Calabi–Yau [Formula: see text]-fold. Also, a semi-conformally flat metric is considered for [Formula: see text] which leads to a dynamical noncommutative spacetime from the viewpoint of noncommutative gravity. Based on the Kahler form of [Formula: see text] the noncommutative star product is defined covariantly on vector bundles over [Formula: see text]. This covariant star product leads to the celebrated Groenewold–Moyal product for trivial vector bundles and their flat connections, such as [Formula: see text]. Hereby, the noncommutative characteristic classes are defined properly and the noncommutative Chern–Weil theory is established by considering the ...
Journal of Geometry and Physics, 2014
A representation of general translation-invariant star products in the algebra of M(C) = lim_N\to... more A representation of general translation-invariant star products in the algebra of M(C) = lim_N\to \infty M_N (C) is introduced which results in the Moyal-Weyl-Wigner quantization. It provides a matrix model for general translation-invariant noncommutative quantum field theories in terms of the noncommutative calculus on differential graded algebras. Upon this machinery a cohomology theory, the so called star-cohomology, with groups H^k_*(C), is worked out which provides a cohomological framework to formulate general translation-invariant noncommutative quantum field theories based on the achievements for the commutative fields, and is comparable to the Seiberg-Witten map for the Moyal case. Employing the Chern-Weil theory via the integral classes of H^k_*(Z) a noncommutative version of the Chern character is defined as an equivariant form which contains topological information about the corresponding translation-invariant noncommutative Yang-Mills theory. Thereby we study the mentio...
The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontolo... more The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontological perspective based on the reality of (semi-) deterministic parallel worlds in the interpretation. It is demonstrated that with thanks to the uncertainty principle there would be no consistent way to specify the correct ontology of the Universe, hence the MWI is subject to an inherent contradiction which claims that the world where we live in is unreal.
It is shown that anti-BRST symmetry is the quantized counterpart of local axial symmetry in gauge... more It is shown that anti-BRST symmetry is the quantized counterpart of local axial symmetry in gauge theories. An extended form of descent equations is worked out which yields a set of modified consistent anomalies.
The theory of alpha_star-cohomology is studied thoroughly and it is shown that in each cohomology... more The theory of alpha_star-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translationinvariant non-commutative quantum field theory is physically equivalent to a Groenewold- Moyal non-commutative quantum field theory.
Translation-invariant products are studied in the setting of alpha^star-cohomology. It is explici... more Translation-invariant products are studied in the setting of alpha^star-cohomology. It is explicitly shown that all quantum behaviors including the Green's functions and the scattering matrix of translation-invariant non-commutative quantum field theories are thoroughly characterized by alpha^star-cohomology classes of the star products.
A gauge invariant partition function is defined for gauge theories which leads to the standard qu... more A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally.
A matrix modeling formulation for translation-invariant noncommutative gauge theories is given in... more A matrix modeling formulation for translation-invariant noncommutative gauge theories is given in the setting of differential graded algebras and quantum groups. Translation-invariant products are discussed in the setting of α-cohomology and it is shown that loop calculations are entirely determined by α-cohomology class of star product in all orders. Noncommutative version of geometric quantization and (anti-) BRST transformations is worked out which leads to a noncommutative description of consistent anomalies and Schwinger terms.
Topological structure of translation-invariant noncommutative Yang-Mills theories are studied by ... more Topological structure of translation-invariant noncommutative Yang-Mills theories are studied by means of a cohomology theory, so called star-cohomology, which plays an intermediate role between de Rham and cyclic (co)homology theory for noncommutative algebras and gives rise to a cohomological formulation comparable to Seiberg-Witten map.
It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantize... more It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantized version of the symmetry of classical gauge theories with respect to different gauge fixing mechanisms.
International Journal of Geometric Methods in Modern Physics, 2016
It is shown that, anti-BRST symmetry is the quantized counterpart of local axial symmetry in gaug... more It is shown that, anti-BRST symmetry is the quantized counterpart of local axial symmetry in gauge theories. An extended form of descent equations is worked out, which yields a set of modified consistent anomalies.
Journal of Mathematical Physics, 2013
The theory of α *-cohomology is studied thoroughly and it is shown that in each cohomology class ... more The theory of α *-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translationinvariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.
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Papers by Amir Abbass Varshovi