scholarly journals An additional remark on unitary evolutions in Fock space

1991 ◽  
pp. 37-38
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Fock Space ◽  
Additional Remark

scholarly journals Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.

scholarly journals Fock-space relativistic coupled-cluster calculation of a hyperfine-induced 1S0→3P0o clock transition in Al+

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Ravi Kumar ◽  
S. Chattopadhyay ◽  
D. Angom ◽  
B. K. Mani
Keyword(s):  
Fock Space ◽  
Coupled Cluster ◽  
Cluster Calculation ◽  
Clock Transition

Toeplitz Operators on the Fock Space with Presymbols Discontinuous on a Thick Set

1996 ◽  
Vol 180 (1) ◽  
pp. 299-315 ◽  
Author(s):  
E. Ram Írez De Arellano ◽  
N. L. Vasilevski
Keyword(s):  
Toeplitz Operators ◽  
Fock Space

The Absurd Injunction to Not Belong and the Bidūn in Kuwait

2020 ◽  
Vol 52 (4) ◽  
pp. 726-732
Author(s):  
Claire Beaugrand
Keyword(s):  
Mobile Phone ◽  
Legal Status ◽  
Personal Data ◽  
Male Voice ◽  
Central System ◽  
Additional Remark ◽  
Special Mention ◽  
The Voice ◽  
Mobile Phone Camera

In a tweet posted on 29 March 2018, a bidūn activist—who was later jailed from July 2019 to January 2020 for peacefully protesting against the inhumane conditions under which the bidūn are living—shared a video. The brief video zooms in closely on an ID card, recognizable as one of those issued to the bidūn, or long-term residents of Kuwait who are in contention with the state regarding their legal status. More precisely, the mobile phone camera focuses on the back of the ID card, on one line with a special mention added by the Central System (al-jihāz al-markazī), the administration in charge of bidūn affairs. Other magnetic strip cards hide the personal data written above and below it. A male voice can be heard saying that he will read this additional remark, but before even doing so he bursts into laughter. The faceless voice goes on to read out the label in an unrestrained laugh: “ladayh qarīb … ladayh qarīna … dālla ʿalā al-jinsiyya al-ʿIrāqiyya” (he has a relative … who has presumptive evidence … suggesting an Iraqi nationality). The video shakes as the result of a contagious laugh that grows in intensity. In the Kuwaiti dialect, the voice continues commenting: “Uqsim bil-Allāh, gaʿadt sāʿa ufakkir shinū maʿanāt hal-ḥatchī” (I swear by God, it took me an hour to figure out the meaning of this nonsense), before reading the sentence again, stopping and guffawing, and asking if he should “repeat it a third time,” expressing amazement at its absurdity. The tweet, addressed to the head of the Central System (mentioned in the hashtag #faḍīḥat Sāliḥ al-Faḍāla, or #scandal Salih al-Fadala), reads: In lam tastaḥī fa-'ktub mā shaʾt (Don't bother, write what you want).

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

scholarly journals Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions

2006 ◽  
Vol 335 (1) ◽  
pp. 79-107 ◽  
Author(s):  
Joaquim Ortega-Cerdà ◽  
Alexander Schuster ◽  
Dror Varolin
Keyword(s):  
Fock Space ◽  
Higher Dimensions

Coupled-cluster method in Fock space. II. Brueckner-Hartree-Fock method

1985 ◽  
Vol 32 (2) ◽  
pp. 743-747 ◽  
Author(s):  
Leszek Z. Stolarczyk ◽  
Hendrik J. Monkhorst
Keyword(s):  
Fock Space ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Coupled Cluster Method ◽  
Hartree Fock

scholarly journals Canonical transformations for fermions in superanalysis

2014 ◽  
Vol 26 (06) ◽  
pp. 1450009
Author(s):  
Joachim Kupsch
Keyword(s):  
Infinite Number ◽  
Orthogonal Group ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Continuous Representation ◽  
Canonical Transformations ◽  
Module Extension ◽  
Bogoliubov Transformations

Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

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