In mathematics, the theta representation is a particular representation of the Heisenberg group of quantum mechanics. It gains its name from the fact...

the theta representation, it acts on the space of holomorphic functions on the upper half-plane; it is so named for its connection with the theta functions...

{\displaystyle {\boldsymbol {\theta }}=\theta \mathbf {e} \,.} It is used for the exponential and logarithm maps involving this representation. Many rotation vectors...

quantum physics Theta representation, a particular representation of the Heisenberg group of quantum mechanics Theta wave, in biology Theta*, a pathfinding...

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces...

{\displaystyle \rho _{n}^{*}(e^{i\theta })=[e^{-in\theta }]=\rho _{-n}(e^{i\theta }).} That is to say, the dual of the representation ρ n {\displaystyle \rho _{n}}...

={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}x\\y\end{bmatrix}}={\begin{bmatrix}x\cos \theta -y\sin \theta \\x\sin...

\left({\begin{pmatrix}e^{i\theta }&0\\0&e^{-i\theta }\end{pmatrix}}\right)=e^{im\theta }+e^{i(m-2)\theta }+\cdots +e^{-i(m-2)\theta }+e^{-im\theta }.} This expression...

{\begin{bmatrix}\theta &0\\0&-\theta \\\end{bmatrix}}=\theta {\begin{bmatrix}1&0\\0&0\\\end{bmatrix}}-\theta {\begin{bmatrix}0&0\\0&1\\\end{bmatrix}}=\theta (e_{1}-e_{2})...

{\displaystyle Ae^{i(\omega t+\theta )}} is an analytic representation of A cos ⁡ ( ω t + θ ) . {\displaystyle A\cos(\omega t+\theta ).} Figure 2 depicts it...

Hn. One representation of the Heisenberg group which is important in number theory and the theory of modular forms is the theta representation, so named...

infinite-dimensional linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and...

data and its latent representation as Prior p θ ( z ) {\displaystyle p_{\theta }(z)} Likelihood p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} Posterior...

Norwegian Resistance Theta representation of the Heisenberg group This disambiguation page lists articles associated with the title Theta group. If an internal...

mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the...

"h" or "b" Voiceless dental fricative (IPA: θ) Theta (Θ and θ), a Greek letter, corresponding to "th" Theta nigrum (ꝋ) for "obiit" ="died" Fita (Ѳ and ѳ)...

(e^{i\theta })=e^{ik\theta },\quad k\in \mathbb {Z} .} We now let Σ {\displaystyle \Sigma } denote a finite-dimensional irreducible representation of K...

and existence of the induced representation. Let ( θ , W θ ) {\displaystyle (\theta ,W_{\theta })} be a linear representation of a subgroup H {\displaystyle...

{\displaystyle f(x;k,\theta )={\frac {x^{k-1}e^{-x/\theta }}{\theta ^{k}\Gamma (k)}}\quad {\text{ for }}x>0{\text{ and }}k,\theta >0.} Here Γ(k) is the...

Phi Theta Kappa (ΦΘΚ or PTK) is an honor society for students of associate degree-granting colleges. Its headquarters are in Jackson, Mississippi and...

spherical coordinate representation, ⟨ θ , φ | l m ⟩ = Y l m ( θ , φ ) {\displaystyle \langle \theta ,\varphi |lm\rangle =Y_{l}^{m}(\theta ,\varphi )} but...

θ } {\displaystyle \left\{1,e^{\pm i\theta }\right\}=\{1,\ \cos \theta +i\sin \theta ,\ \cos \theta -i\sin \theta \}} where i is the standard imaginary...

Q_{1}={\begin{bmatrix}1&0&0&0\\0&\cos(\theta )&\sin(\theta )&0\\0&-\sin(\theta )&\cos(\theta )&0\\0&0&0&1\end{bmatrix}}=\exp \left(\theta {\begin{bmatrix}0&0&0&0\\...

{\begin{aligned}R_{x}(\theta )&=e^{(-i\theta X/2)}=\cos(\theta /2)I-i\sin(\theta /2)X={\begin{bmatrix}\cos \theta /2&-i\sin \theta /2\\-i\sin \theta /2&\cos \theta...

mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties...

\left({\frac {\theta }{2}}\right)-i\sigma _{3}\sin \left({\frac {\theta }{2}}\right)\right]\sigma _{3}\left[\cos \left({\frac {\theta }{2}}\right)+i\sigma...

ISBN 9783110885583 Lion, G.; Vergne, M. (1980), The Weil representation, Maslov index and theta series, Progress in Mathematics, vol. 6, Birkhäuser, ISBN 3-7643-3007-4...

{\begin{aligned}x(\theta )&=(R-r)\cos \theta +d\cos \left({R-r \over r}\theta \right)\\y(\theta )&=(R-r)\sin \theta -d\sin \left({R-r \over r}\theta \right)\,...

t+\theta )}\ \ =\ e^{j|\omega |t}\cdot e^{j\theta },&{\text{if}}\ \omega >0,\\e^{-j(\omega t+\theta )}=\ e^{j|\omega |t}\cdot e^{-j\theta },&{\text{if}}\...

group Mumford-Tate group Mumford measure Mumford vanishing theorem Theta representation Manin–Mumford conjecture Horrocks–Mumford bundle Deligne–Mumford...