The Eichler Commutation Relation and the continuous spectrum of the weil representation

1979 ◽  
pp. 211-244 ◽  
Author(s):  
Stephen Rallis
Keyword(s):  
Continuous Spectrum ◽  
Commutation Relation ◽  
Weil Representation

scholarly journals The commutation relation i[Y, Z] = 2Y and the absolutely continuous spectrum of Y

1982 ◽  
Vol 23 (4) ◽  
pp. 420-427
Author(s):  
J. V. Corbett
Keyword(s):  
Continuous Spectrum ◽  
Commutation Relation ◽  
Singular Continuous Spectrum ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
System Of Imprimitivity

AbstractA relation between positive commutators and absolutely continuous spectrum is obtained. If i[Y, Z] = 2Y holds on a core for Z and if Y is positive then we have a system of imprimitivity for the group on , from which it follows that Y has no singular continuous spectrum.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

scholarly journals Scheme for Proving the Bosonic Commutation Relation Using Single-Photon Interference

2008 ◽  
Vol 101 (26) ◽  
Author(s):  
M. S. Kim ◽  
H. Jeong ◽  
A. Zavatta ◽  
V. Parigi ◽  
M. Bellini
Keyword(s):  
Commutation Relation ◽  
Single Photon

scholarly journals Nontrivial topology in the continuous spectrum of a magnetized plasma

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Jeffrey B. Parker ◽  
J. W. Burby ◽  
J. B. Marston ◽  
Steven M. Tobias
Keyword(s):  
Continuous Spectrum ◽  
Magnetized Plasma ◽  
Nontrivial Topology

scholarly journals Geometric Weil representation in characteristic two

2011 ◽  
Vol 11 (2) ◽  
pp. 221-271 ◽  
Author(s):  
Alain Genestier ◽  
Sergey Lysenko
Keyword(s):  
Weil Representation ◽  
Closed Field ◽  
Triangulated Category ◽  
Algebraically Closed Field ◽  
Witt Vectors ◽  
Suitable Sense ◽  
Characteristic Two ◽  
Greenberg Realization ◽  
Geometric Analogue

AbstractLet k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack Ĝ over k, the metaplectic extension of the Greenberg realization of $\operatorname{\mathbb{S}p}_{2n}(R)$. We also construct a geometric analogue of the Weil representation of Ĝ, this is a triangulated category on which Ĝ acts by functors. This triangulated category and the action are geometric in a suitable sense.

The continuous spectrum of hydrogen

1927 ◽  
Vol 203 (5) ◽  
pp. 737-738
Author(s):  
G.F.S.
Keyword(s):  
Continuous Spectrum

α-Adrenoceptor agonists and the Ca2+-dependence of smooth muscle contraction: evidence for subtypes of receptors or for agonist-dependent differences in the agonist-receptor interaction?

1985 ◽  
Vol 68 (s10) ◽  
pp. 55s-63s ◽  
Author(s):  
John C. McGrath
Keyword(s):  
Smooth Muscle ◽  
Muscle Contraction ◽  
Continuous Spectrum ◽  
Contractile Response ◽  
Nitrilotriacetic Acid ◽  
Smooth Muscle Contraction ◽  
Receptor Type ◽  
Receptor Interaction ◽  
Initial Transient ◽  
Adrenoceptor Agonists

1. The effects of varying [Ca2+]o on the contraction of smooth muscle by different α-adrenoceptor agonists were examined on rat isolated anococcygeus muscle. Agonists were tested in the presence of various [Ca2+]o or ‘Ca2+-re-addition curves’ were constructed. In some experiments the [Ca2+]free was buffered with EGTA and nitrilotriacetic acid. The components of the response which were revealed were further analysed by using drugs which modify Ca2+ mobilization. 2. Three separate elements in the contractile response were identified: (i) an initial transient contraction, due to intracellular Ca2+ release could be isolated with [Ca2+]o between 1 nmol/l and 3 μmol/l (this could be obtained only with noradrenaline, phenylephrine and amidephrine); (ii) a nifedipine-sensitive response requiring [Ca2+]o of 3 μmol/l or more; (iii) a nifedipine-resistant response requiring [Ca2+]o of 100 μmol/l or more. Presumably (ii) and (iii) involve the entry of Ca2+o: they could be obtained with all agonists tested, including these above, methoxamine, indanidine and xylazine. 3. The results are discussed in relation to the possibility of distinct types of response and their relationship to subgroups of receptors or agonists. It is concluded that there is a continuous spectrum of activity across the agonist range and that this is likely to correlate with ‘efficacy’ at a single α1 receptor type.

(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1808-1818
Author(s):  
S. KUWATA ◽  
A. MARUMOTO
Keyword(s):  
Irreducible Representation ◽  
Harmonic Oscillator ◽  
Linear Algebra ◽  
Commutation Relation ◽  
Complex Number ◽  
Single Mode ◽  
Equation Of Motion ◽  
Sufficient Condition ◽  
Special Linear ◽  
Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

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