Ufuk Kayserilioglu | Bogazici University (original) (raw)
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We propose a deformed algebra of creation and annihilation operators relating quark-lepton states... more We propose a deformed algebra of creation and annihilation operators relating quark-lepton states. A diagonal mass operator with three parameters together with the three deformation parameters of the algebra gives a reasonable fit to observed quark-lepton masses.
Journal of Physics A-mathematical and General, 1998
The particle decay problem in the random-set approach leads naturally to the q-Poisson distributi... more The particle decay problem in the random-set approach leads naturally to the q-Poisson distribution. Motivated by the fact that in the classical quantum mechanical description of particle decay one ends up with a composite system, we construct a Hilbert space using the eigenstates of the average particle number operator N. In this approach, time is represented by integer multiples of an observation quantum 0305-4470/31/46/003/img1. It is shown that these considerations lead to the redefined q-oscillator and an element of 0305-4470/31/46/003/img2 acts like a reversal operator on n time-ordered states.
Physics Letters A, 1999
... 253 (1999) 132134 PHYSICS LETTERS A Fermionic random sets and qoscillators U. Kayserilioglu, ... more ... 253 (1999) 132134 PHYSICS LETTERS A Fermionic random sets and qoscillators U. Kayserilioglu, J. Kornfilt, G. Unel, MB Unlu Physics Department, Bogazici University, Bebek, Istanbul, Turkey ... [2]. Two events N( and N2 are said to be ... [ 2 ]. S is our source set of M elements and ...
We define a 3-generator algebra obtained by replacing the commutators by anticommutators in the d... more We define a 3-generator algebra obtained by replacing the commutators by anticommutators in the defining relations of the angular momentum algebra. We show that integer spin representations are in one to one correspondence with those of the angular momentum algebra. The half-integer spin representations, on the other hand, split into two representations of dimension j + 1 2 . The anticommutator spin algebra is invariant under the action of the quantum group SOq(3) with q = −1.
The particle algebras generated by the creation/annihilation operators for bosons and for fermion... more The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.
We propose a deformed algebra of creation and annihilation operators relating quark-lepton states... more We propose a deformed algebra of creation and annihilation operators relating quark-lepton states. A diagonal mass operator with three parameters together with the three deformation parameters of the algebra gives a reasonable fit to observed quark-lepton masses.
This work is dedicated to my loving wife Emi for all her support and understanding; to my wise an... more This work is dedicated to my loving wife Emi for all her support and understanding; to my wise and patient mentor Metin Arık for teaching me a lot of what I know and to my parents who have shown me how to think scientifically about nature. iv ABSTRACT QUANTUM GROUP STRUCTURES ASSOCIATED WITH INVARIANCES OF SOME PHYSICAL ALGEBRAS In this study, the anticommuting spin algebra is introduced and it is shown to be invariant under the action of the quantum group SO q=−1 (3). Furthermore, its representations and Hopf algebra structure are studied and found to be closely resemble the similar results for the angular momentum algebra. The invariance properties of the bosonic and fermionic oscillator algebras under inhomogeneous transformations are also studied. The bosonic inhomogeneous symplectic group, BISp(2d, R) , and the fermionic inhomogeneous orthogonal group, F IO(2d, R) , are defined as the inhomogeneous invariance quantum groups of these algebras. The sub(quantum)groups and contractions of these quantum groups are studied as a source for new quantum groups. Finally, the fermionic inhomogeneous orthogonal quantum group is defined for odd number of dimensions and its sub(quantum)groups and contractions are studied. inho v OZET BAZI FİZİKSEL CEBİRLERİN DEGİŞMEZLİGİİLEİLGİLİ KUANTUM GRUP YAPILARI Buçalışmada, ters-degişmeli spin cebri tanımlanmış ve bu cebrin SO q=−1 (3)
We propose a deformed algebra of creation and annihilation operators relating quark-lepton states... more We propose a deformed algebra of creation and annihilation operators relating quark-lepton states. A diagonal mass operator with three parameters together with the three deformation parameters of the algebra gives a reasonable fit to observed quark-lepton masses.
Journal of Physics A-mathematical and General, 1998
The particle decay problem in the random-set approach leads naturally to the q-Poisson distributi... more The particle decay problem in the random-set approach leads naturally to the q-Poisson distribution. Motivated by the fact that in the classical quantum mechanical description of particle decay one ends up with a composite system, we construct a Hilbert space using the eigenstates of the average particle number operator N. In this approach, time is represented by integer multiples of an observation quantum 0305-4470/31/46/003/img1. It is shown that these considerations lead to the redefined q-oscillator and an element of 0305-4470/31/46/003/img2 acts like a reversal operator on n time-ordered states.
Physics Letters A, 1999
... 253 (1999) 132134 PHYSICS LETTERS A Fermionic random sets and qoscillators U. Kayserilioglu, ... more ... 253 (1999) 132134 PHYSICS LETTERS A Fermionic random sets and qoscillators U. Kayserilioglu, J. Kornfilt, G. Unel, MB Unlu Physics Department, Bogazici University, Bebek, Istanbul, Turkey ... [2]. Two events N( and N2 are said to be ... [ 2 ]. S is our source set of M elements and ...
We define a 3-generator algebra obtained by replacing the commutators by anticommutators in the d... more We define a 3-generator algebra obtained by replacing the commutators by anticommutators in the defining relations of the angular momentum algebra. We show that integer spin representations are in one to one correspondence with those of the angular momentum algebra. The half-integer spin representations, on the other hand, split into two representations of dimension j + 1 2 . The anticommutator spin algebra is invariant under the action of the quantum group SOq(3) with q = −1.
The particle algebras generated by the creation/annihilation operators for bosons and for fermion... more The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.
We propose a deformed algebra of creation and annihilation operators relating quark-lepton states... more We propose a deformed algebra of creation and annihilation operators relating quark-lepton states. A diagonal mass operator with three parameters together with the three deformation parameters of the algebra gives a reasonable fit to observed quark-lepton masses.
This work is dedicated to my loving wife Emi for all her support and understanding; to my wise an... more This work is dedicated to my loving wife Emi for all her support and understanding; to my wise and patient mentor Metin Arık for teaching me a lot of what I know and to my parents who have shown me how to think scientifically about nature. iv ABSTRACT QUANTUM GROUP STRUCTURES ASSOCIATED WITH INVARIANCES OF SOME PHYSICAL ALGEBRAS In this study, the anticommuting spin algebra is introduced and it is shown to be invariant under the action of the quantum group SO q=−1 (3). Furthermore, its representations and Hopf algebra structure are studied and found to be closely resemble the similar results for the angular momentum algebra. The invariance properties of the bosonic and fermionic oscillator algebras under inhomogeneous transformations are also studied. The bosonic inhomogeneous symplectic group, BISp(2d, R) , and the fermionic inhomogeneous orthogonal group, F IO(2d, R) , are defined as the inhomogeneous invariance quantum groups of these algebras. The sub(quantum)groups and contractions of these quantum groups are studied as a source for new quantum groups. Finally, the fermionic inhomogeneous orthogonal quantum group is defined for odd number of dimensions and its sub(quantum)groups and contractions are studied. inho v OZET BAZI FİZİKSEL CEBİRLERİN DEGİŞMEZLİGİİLEİLGİLİ KUANTUM GRUP YAPILARI Buçalışmada, ters-degişmeli spin cebri tanımlanmış ve bu cebrin SO q=−1 (3)