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pro vyhledávání: '"Jadczyk, Arkadiusz"'
Autor:
Jadczyk, Arkadiusz
Publikováno v:
Mathematics 2024, 12(8), 1140
We geometrically derive the explicit form of the Unitary representation of the Poincare group and use it to apply speed-of-light boosts to simple polarization basis to end up with Hawton-Baylis photon position operator with commuting components. We g
Externí odkaz:
http://arxiv.org/abs/2401.14217
Autor:
Jadczyk, Arkadiusz
Publikováno v:
Advances in Applied Clifford Algebras, vol 33, 15-33, 2023 \vol 33 \pages 15--33 \yr 2023
For each quadratic form Q in Quad(V) over a given vector space over a field R we have the Clifford algebra Cl(V,Q) defined as the quotient T(V)/I(Q) of the tensor algebra T(V) over the two-sided ideal generated by expressions of the form $x x-Q(x),x
Externí odkaz:
http://arxiv.org/abs/2103.09767
Autor:
Jadczyk, Arkadiusz, Szulga, Jerzy
Publikováno v:
Electronic Journal of Linear Algebra, 2016, Volume 31, pp. 794-833
Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a $G$-skew symmetric matrix, underlining its unconnectedness at one of it
Externí odkaz:
http://arxiv.org/abs/1611.06379
Autor:
Jadczyk, Arkadiusz
We describe the action of the symplectic group on the homogeneous space of squeezed states (quantum blobs) and extend this action to the semigroup. We then extend the metaplectic representation to the metaplectic (or oscillator) semigroup and study t
Externí odkaz:
http://arxiv.org/abs/1510.04671
Autor:
Jadczyk, Arkadiusz
In a recent work, Kryuchkov, Suslov and Vega-Guzman [20013 J. Phys. B: At. Mol. Opt. Phys. 46 104007] described a multi-parameter family of minimum-uncertainty states satisfying the time-dependent Schrodinger equation for the harmonic oscillator. We
Externí odkaz:
http://arxiv.org/abs/1502.06444
Autor:
Jadczyk, Arkadiusz
Publikováno v:
Rep. Math. Phys. 76 No 2, (2015), 149-158
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading
Externí odkaz:
http://arxiv.org/abs/1501.07483
Autor:
Jadczyk, Arkadiusz, Szulga, Jerzy
Publikováno v:
Reports on Mathematical Physics, 74(1), 2014, 39-44
We comment on the article by M. Ozdemir and M. Erdogdu. We indicate that the exponential map onto the Lorentz group can be obtained in two elementary ways. The first way utilizes a commutative algebra involving a conjugate of a semi-skew-symmetric ma
Externí odkaz:
http://arxiv.org/abs/1412.5581
Autor:
Jadczyk, Arkadiusz
Publikováno v:
International Journal of Geometric Methods in Modern Physics, Vol. 11 (2014) 1460019
Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by J. Kijowski and the EEQT method. It is suggested that for free particles the two methods may lead to the same result.
Externí odkaz:
http://arxiv.org/abs/1402.6119
Autor:
Jadczyk, Arkadiusz
Publikováno v:
Advances in Applied Clifford Algebras, Volume 22, Issue 3 , 2012, pp 689-701
In this paper we give a brief review of the pseudo-Riemannian geometry of the five-dimensional homogeneous space for the conformal group O(4,2). Its topology is described and its relation to the conformally compactified Minkowski space is described.
Externí odkaz:
http://arxiv.org/abs/1111.5540
Autor:
Jadczyk, Arkadiusz
Publikováno v:
Reports on Mathematical Physics, Vol. 69, Issue 2, 2012, pp 179-195
We review and further analyze Penrose's 'light cone at infinity' - the conformal closure of Minkowski space. Examples of a potential confusion in the existing literature about it's geometry and shape are pointed out. It is argued that it is better to
Externí odkaz:
http://arxiv.org/abs/1107.0933