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L_{E-H}=\epsilon _{abcd}R^{ab}e^{c}e^{d}+dB, \label{EH}

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- { \textstyle \frac { 1 } { 2 } } \omega ^ { + a b } _ { \hat { 0 } } \sigma _ { a b } \epsilon _ { I } = \gamma ^ { i } ( - { \textstyle \frac { i } { 4 } } e ^ { 3 \phi } \partial _ { \hat { \imath } } \overline { \lambda } \gamma ^ { 0 } \epsilon _ { I } ) \, .

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tokenized

- \kappa ^ { 2 } g ^ { 2 } \alpha ^ { \prime } \left( \frac { 7 1 1 6 8 } { 5 9 0 4 9 } \right) ( A ^ { \mu } A _ { \mu } ) ^ { 2 } .

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normalized

\Phi _ A ^ { a b c } = 2 \varepsilon ^ { a \underline { b } } \rho _ A ^ { \underline { c } }

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tokenized

\int _ { C } T _ { \mu \nu } k ^ { \mu } k ^ { \nu } d \lambda \ge 0

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normalized

{\cal W}_{\rm PM}(\phi ) =\frac{m^2}{4\lambda}\,\phi-\frac{\lambda}{3}\,\phi^3\,,\label{PS}

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{ \frac { 2 m } { N } } - 2 m _ { 1 } = r - \ell \; .

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normalized

p(\beta,L)=\rho(\beta,L)= \frac{1}{L^{2}}f'\left(\frac{\beta}{L}\right)\;.

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\tilde { S } _ { 0 } ^ { L } \left [ A _ { \mu } ^ { a } , B _ { a } ^ { \mu \nu } \right ] = \frac { 1 } { 2 }

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tokenized

d s ^ { 2 } = h ( l ) d t ^ { 2 } - \frac { d l ^ { 2 } } { h ( l ) } - d y ^ { 2 } - d z ^ { 2 }

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normalized

(\stackrel{(0)}{S},\stackrel{(0)}{S})=0\longrightarrow(S,S)=0 \label{fullmasterequation}.

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c=\frac{1}{1-\hat{u}}~~, \hspace{1cm}b=64 e^{2 \pi i\tau}.\label{15}

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A _ { l } = \sum _ { k } \alpha _ { l k } ^ { * } a _ { k } - \beta _ { l k } ^ { * } a _ { k } ^ { \dagger } \; .

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normalized

\varphi(n)=\frac{\sin\vartheta n}{\sin\vartheta} \ \ .

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U^{\dagger}(\Lambda)\vec{\jmath}\,(P)U(\Lambda)={\cal R}_W(\Lambda,P)\vec{\jmath}.

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\delta \left( Z _ { \; \; b _ { 1 } } ^ { a _ { 0 } } { \cal P } _ { a _ { 0 } } \right) = - D _ { \; \; b _ { 1 } } ^ { a _ { 1 } } \pi _ { a _ { 1 } } .

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normalized

0 = \int _ { K 3 } \eta _ { I J } F ^ { I } \wedge F ^ { J } = m ^ { A I } m ^ { B J } \rho _ { A B } \, \eta _ { I J } \ ,

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normalized

n ( x ) = \Psi ^ { \dagger } ( x ) \Psi ( x ) ,

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tokenized

S _ { \mathrm { t o t a l } } = S + S _ { \mathrm { s o u r c e } } ~ ,

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normalized

\hat { \hat { \epsilon } } ^ { \hat { \hat { \mu } } _ { 0 } \ldots \hat { \hat { \mu } } _ { 1 0 } } = 1 .

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normalized

{ \cal N } _ { A B } = \frac { \partial } { \partial \bar X ^ A } \frac { \partial } { \partial \bar X ^ B } \bar F \ .

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tokenized

n_{i}\longrightarrow n_{i}+q_{i}m,\;\;m\in{\bf Z}\label{3.210}

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m _ t / v \sim m _ b / w \sim ( 1 8 0 G e V / 2 4 6 G e V ) .

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\bar { K } ( z ; i _ { s } ) \bar { Z } ( z ) G ( i _ { s } ) = Z ( z ^ { \prime } ) ^ { t } \, ,

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( { \bf u } _ { I } , [ D _ { a } , \Delta _ { f } ] { \bf u } _ { J } ) = 4 C _ { ( I J ) a }

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normalized

\{ Q ^ a _ \alpha , Q ^ b _ \beta \} = 2 \omega ^ { a b } \gamma _ { \alpha \beta } ^ \mu P _ \mu + \gamma _ { \alpha \beta } ^ \mu Z ^ { a b } _ \mu

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m_l/M={\rm Log} \left( \frac {F_l}{F_0}\right) .\label{mass}

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T^{(1,\dots ,N)}_{k}\left( \theta _{1},\dots ,\theta _{N}\right)

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{\Pi}^{(-N)}=p^{(-N)} [ {\bf 1} - {\pi}^{(j^{(-N)})}],

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[ D, Q_{+{1\over 2}} ] = {1\over 2} Q_{+{1\over 2}} \ , \qquad [ D,S_{-{1\over 2}} ] = -{1\over 2} S_{-{1\over 2}} \ .

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\label{n5.9}c_0=\int_{\bar{B}}{\bar h}^{1/2} d^2x=\mbox{Vol}~\bar{\cal B},

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w = \underbrace { r _ { \epsilon } \cdots r _ { 0 } r _ { 1 } } _ { l } ,

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r(n;s)=\int_s^\infty (x-s) \psi(q_0,\cdots,q_n)\, dx\label{r_integral}

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\eta _{2}\,=\,\frac{1\,-\,{\frac{\partial _{+}\,\hat{\varphi}}{\partial_{-}\,\hat{\varphi}}}}{1\,+\,{\frac{\partial _{+}\,\hat{\varphi}}{\partial_{-}\,\hat{\varphi}}}}\;\;.

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\label{symm:metr1} ds^2 = dy^A dy^B \eta_{AB}

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M _ { \psi } ^ { 2 } = { \frac { d ^ { 2 } } { ( \pi \alpha ^ { \prime } ) ^ { 2 } } } \ ,

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\hat X_{i} \equiv\sqrt{ X_{i}^{2}+r_{0}^{2}}, \ \ \ X_{i}=(X,Y,P).

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\left( b + a \nabla ^ { 2 } \right) \nabla ^ { 2 } G ( \bar { x } , \bar { y } ) \, = \, \delta ^ { 2 } (

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N t _ { 1 1 } \equiv k \ { \rm m o d } \ N \, .

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\label{breflect} \eta\sim \lambda_1\, e^{-i\omega t}\left(e^{ikx}+K_B\, e^{-ikx}\right) ,

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\label{cyl3} \lambda_i(\tau,x+2\pi) = \lambda_{Q(i)}(\tau,x)~.

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X _ \tau = F _ 1 X _ \sigma - F _ 2 X _ \sigma - F _ 3 X _ \tau ,

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\label{density_HO}\rho(q)=1,\;\; \rho(Q,t)={1\over 2\pi \sin t}.

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F _ { i } = F _ { i } ( \phi ) \ ; \ G _ { i } = G _ { i } ( \phi ) \ ; \ D _ { i } = D _ { i } ( \phi )

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normalized

( d s ) ^ { 2 } = - [ d \tau ^ { 2 } - ( M \tau ) ^ { 2 } d x ^ { 2 } ] ; \hspace { 0 . 3 c m } 0 \le \tau < \infty

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normalized

\sum _ { i } { \cal C } _ { i } N _ { i } ^ { 2 } = \sum _ { i \neq j } { \cal L } _ { i j } | N _ { i } N _ { j } | + \sum _ { i } { \cal K } _ { i } N _ { i } ^ { 2 } .

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{\tilde D}_{m}= D_{m}-\frac{1}{2}m\Gamma_{m}

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D = - ( \partial _ \mu + i A _ \mu ) ( \partial _ \mu + i A _ \mu ) + \sigma .

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\Delta \sigma ( A ) = \Delta \sigma \left( 1 + A ^ { 2 } / 4 m ^ { 4 } ( \Delta \sigma ) ^ { 4 } \right) ^ { 1 / 2 } \ .

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normalized

{ Q } ( \iota _ * { F } ) = { Q } ( \iota _ * { E } ) + { Q } ( \iota _ * { G } ) \, .

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tokenized

G _ F = M _ { \rm W } ^ { - 2 } \sim 1 0 ^ { - 5 } \ \ \mbox { G e V } ^ { - 2 }

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U_{4\pi} = 4(\delta_{ij} \delta_{kl}+ cyclic) f^{\prime\prime}(v^2)

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E ^ \prime = - B G ^ { - 1 } B - B = { B _ { 1 2 } ^ 2 \over \det ( G ) } ~ G - B ~ .

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tokenized

\phi _ i = x _ i / l _ s ^ 2 ~ , ~ \phi ^ 8 = x _ { 1 1 } / l _ s ^ 2 ~ , ~ u = v / l _ s ^ 2 ,

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{ \cal P } _ { a } = p _ { a } \qquad { \cal J } _ { a } = \epsilon _ { a b c } x ^ { b } p ^ { c } + J _ { a } \, ,

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normalized

r _ { - } = - q _ { - } \circ \left( q _ { - } - \bar { M } \circ q _ { + } \right) ^ { - 1 } .

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normalized

\hat { c } _ { - \alpha } = e ^ { - i q \alpha } \sum _ { \beta \in \Lambda _ { R } } | \beta + \bar { p } > < \beta + \bar { p } |

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tokenized

W _ { \perp } = e x p \{ \frac { i } { 2 } \operatorname { t a n } ^ { - 1 } \frac { p _ { \perp } } { m } \mathrm { \boldmath ~ \gamma ~ } _ { \perp } \cdot { \bf p } _ { \perp } \}

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normalized

[ { \cal E } ^ \alpha _ i ( x ) , A ^ \beta _ j ( x ' ) ] = i \delta ^ { \alpha \beta } \delta _ { i j } \delta ( x - x ' ) ,

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tokenized

E _ c = - 2 \frac { n l r _ + ^ { n - 1 } V o l ( \Sigma _ n ) } { 1 6 \pi G R } .

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tokenized

\operatorname { l n } \, [ \alpha _ { a ( M _ { T } ) } / \alpha _ { a ( M _ { Z } ) } ] , \, \, \operatorname { l n } \, [ \alpha _ { a ( M _ { X } } ) / \alpha _ { a ( M _ { T } ) } ]

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normalized

| \Phi \rangle = | \Phi ^ { ( 0 ) } \rangle + a _ { _ U } | \Phi ^ { ( 1 ) } \rangle \, ,

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u_a v^a = 0, \hspace{1.5em} v_a v^a = -2.%\label{U_VNorm}

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\lambda\equiv\tau_2/\tau_1=\theta g_{\rm YM}^2/8\pi^2~.

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\left| \left. b,\frac{1}{2},a,\frac{1}{2}\right| l,k-l,n\right\rangle \: .

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x_d^{(1/2)}(u,\xi)={x(u,\xi)\,x(u+\omega_{1},\xi)\over x(\omega_{1},\xi)}.

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G \left( \xi \right) = \frac { 3 } { 8 } \xi ^ { - 4 } - \frac { 7 } { 8 } \, \frac { 1 } { 1 2 0 } + O \left( \xi ^ { 2 } \right) ,

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normalized

S _ { \mathrm { H } } ^ { 2 } - S _ { \mathrm { \Lambda } } ^ { 2 } = S _ { \mathrm { B H } } ( 2 S _ { \mathrm { B V } } - S _ { \mathrm { B H } } ) .

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normalized

a _ { q } = a f ( \hat { n } ) , ~ ~ ~ a _ { q } ^ { \dag } = f ( \hat { n } ) a ^ { \dag }

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normalized

\Pi^{(2)}_{PV}(k^2,m)=\Pi^{(1)}(k^2,m)-\frac{g^2}{4\pi} sgn(M)\ .\label{2.9}

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[ e _ { a } , A _ { b } ^ { i } ( \vec { x } ) ] _ { D } = g c _ { a b c } A _ { c } ^ { i } ( \vec { x } )

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normalized

\widehat { \cal M } _ { i } = K _ { i j } ( \widehat { \Delta } ) s \widehat { \Delta } _ { j } \ \ .

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tokenized

W _ { t r e e } = \lambda \Phi Q { \widetilde Q } ~ ,

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normalized

t=\int_0^\tau d\tau'\,e(\tau'),\quad T=\int_0^1 d\tau\,e(\tau)

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g = e ^ { \frac { i } { 2 } \theta _ { \mathrm { L } } \sigma _ { 2 } } e ^ { \frac { 1 } { 2 } r \sigma _ { 1 } } e ^ { \frac { i } { 2 } \theta _ { \mathrm { R } } \sigma _ { 2 } } ,

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normalized

\eta \cdot k = - i k ^ { 2 } \pm i \sqrt { { \frac { ( k ^ { 2 } + \eta ^ { 2 } ) ( k ^ { 2 } + i \epsilon ) } { 1 - \lambda } } } .

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normalized

\label{sequestered}K\ =\ -3\log \left[\, -\frac{1}{3} Q^+ Q \ +\ f(H^+, H)\,\right]\ .\label{K_RS}

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\vec {k}_1^{ex}= (0,0,0,1):\,\,\,\,\,|C_4|=4,

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\label{dm}\frac{d G(\rho_2)}{d \rho_2} = - \frac{g_2^2}{8 \pi^2} \rho_2 G(\rho_2)~.

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\Omega = D A + A \wedge A \doteq D X ^ { M } \wedge D X ^ { N } \Omega _ { M N } .

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normalized

K^m_A \frac{\partial}{\partial z_m} = \frac{\partial}{\partial \xi_A} .

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\frac { d ^ { 2 } \xi ^ { \mu } } { d t ^ { 2 } } = - R _ { 0 k 0 } ^ { \mu } \xi ^ { k } - \frac { 1 } { 2 } [

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tokenized

S_iW_\alpha\bar W_{\dot \alpha},\bar S_iW_\alpha\bar W_{\dot \alpha}

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{ \partial L \over \partial t } = \{ B _ 1 , L \}

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tokenized

{\cal F}_2 %= - \frac{{\rm ln}Z_2}{\beta V}= \frac{g_r^2M_rT^2}{(4\pi)^2}\left(\frac{1}{x^2}[g_2(x,-r)-g_2(x,r)]^2+[x-h_2(x,-r)-h_2(x,r)]^2\right)\;.\label{F2}

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- \partial ^ 2 _ { \rho } \chi + \frac { 2 } { \rho ^ 2 } \chi - \frac { \Lambda ^ 2 } { k ^ 2 } ( 1 - \frac { l ( l + 1 ) k ^ 2 } { E ^ 2 } ) \chi = 0

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tokenized

\tilde G ^ { - 1 } ( k ) = \sum _ { s } c ( s ) e ^ { - i k s }

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tokenized

\label{18}\gamma = \mp f_{\infty} \left( f_{\infty} + {v_0 ^2 \over 2 f_0} \right)

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c _ { 0 j } ^ { N } \ = \ \operatorname { e x p } \left[ \frac { 1 } { 2 } \sum _ { n = 1 } ^ { j } \operatorname { l n } \frac { 1 - n / ( N + 1 ) } { 1 + n / ( N + 1 ) } \right] \ = \

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normalized

\xi_j = \sqrt{\kappa} z_j\ , \label{wkba}

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\varepsilon_0 = \langle 0| {\cal H} |0 \rangle = - \sum_{{\bf {p}}, \sigma} \epsilon_{{\bf {p}} \sigma}^{(-)},

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\psi _ { n } ( x ) = x B _ { n - 1 } ( { 1 + \eta \over \sqrt { 1 + 2 \eta } } - x ^ { 2 } )

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tokenized

p _ \Lambda = \sum _ { \ell = 1 } ^ { n } c _ { \Lambda \Lambda ^ { ( \ell ) } } \, s _ { \Lambda ^ { ( \ell ) } } ,

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tokenized

\chi ( T M ) = \chi ( M ) \equiv \sum _ { k } ( - 1 ) ^ { k } b _ { k } ( M ) ,

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normalized

\Delta _ F ( x , x ' ) = \int \, { d ^ 4 k \over ( 2 \pi ) ^ 4 } { e ^ { i k x } \over k ^ 2 + m ^ 2 - i \epsilon } \, ,

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tokenized

\triangle = { \frac { 1 } { \sqrt { g } } } \sum _ { j j ^ { \prime } } { \frac { \partial } { \partial t _ { j } } } \; \left( \, \sqrt { g } \, g ^ { j j ^ { \prime } } \, { \frac { \partial } { \partial t _ { j ^ { \prime } } } } \, \right)

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normalized

\Gamma = A _ { h } \frac { 1 } { ( e ^ { \frac { \omega } { T _ { H } } } - 1 ) } \frac { d ^ 3 k } { ( 2 \pi ) ^ 3 } ,

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tokenized

{ \cal R } = { \cal R } _ { r } \operatorname { s i n } \eta , ~ ~ ~ \tau = { \cal R } _ { r } ( 1 - \operatorname { c o s } \eta ) .

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normalized

{ \widehat M } _ { P } ^ { 2 } \sim { \frac { r ^ { 2 } } { ( \alpha ^ { \prime } ) ^ { 2 } } } ~ ,

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normalized

\psi _ { \scriptscriptstyle W } = \frac { 1 } { 2 } ( \psi \pm \gamma _ 5 \psi \gamma _ { 2 1 } ) .

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tokenized