如果你也在 怎样代写弦论string theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。弦论string theory在物理学中是一个理论框架，其中粒子物理学中的点状粒子被称为弦的一维物体取代。弦理论描述了这些弦如何在空间传播并相互作用。在大于弦的距离尺度上，弦看起来就像一个普通的粒子，其质量、电荷和其他属性由弦的振动状态决定。在弦理论中，弦的许多振动状态之一对应于引力子，一种携带引力的量子力学粒子。因此，弦理论是一种量子引力的理论。
弦论string theory是一个广泛而多样的学科，它试图解决基础物理学的一些深层次问题。弦理论为数学物理学贡献了许多进展，这些进展被应用于黑洞物理学、早期宇宙宇宙学、核物理学和凝聚态物理学中的各种问题，它也刺激了纯数学的一些重大发展。由于弦理论有可能提供对引力和粒子物理学的统一描述，它是万物理论的候选者，是描述所有基本力量和物质形式的独立数学模型。尽管在这些问题上做了很多工作，但目前还不知道弦理论在多大程度上描述了现实世界，也不知道该理论在选择其细节方面允许多大的自由度。
my-assignmentexpert™ 弦论string theory作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的弦论string theory作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此弦论string theory作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。
想知道您作业确定的价格吗? 免费下单以相关学科的专家能了解具体的要求之后在1-3个小时就提出价格。专家的 报价比上列的价格能便宜好几倍。
my-assignmentexpert™ 为您的留学生涯保驾护航 在物理physics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的弦论string theory代写服务。我们的专家在物理physics代写方面经验极为丰富，各种弦论string theory相关的作业也就用不着 说。
我们提供的弦论string theory及其相关学科的代写，服务范围广, 其中包括但不限于:
物理代写|弦论代写string theory代考|超引力代写supergravity|Commutation relations
The quantization of the bosonic coordinates $X^{\mu}$ is found to be given by the commutation relations
$$
\left[\partial_{\tau} X^{\mu}(\sigma), X^{\nu}\left(\sigma^{\prime}\right)\right]=-i \pi \delta\left(\sigma-\sigma^{\prime}\right) \eta^{\mu \nu} .
$$
These lead to the commutation relations
$$
\begin{aligned}
& {\left[\alpha_{n}^{\mu}, \alpha_{m}^{\nu}\right]=n \delta_{n+m, 0} \eta^{\mu \nu}, \quad \text { open string. } } \
{\left[\alpha_{n}^{\mu}, \alpha_{m}^{\nu}\right] } &=\left[\tilde{\alpha}{n}^{\mu}, \widetilde{\alpha}{m}^{\nu}\right] \
&=n \delta_{n+m, 0} \eta^{\mu \nu}, \quad\left[\alpha_{n}^{\mu}, \tilde{\alpha}{m}^{\nu}\right]=0, \quad \text { closed string. } \end{aligned} $$ Similarly the quantization of the fermionic coordinates $\psi{A}^{\mu}$ is found to be given by the anticommutation relations
$$
\left{\psi_{A}^{\mu}(\sigma), \psi_{B}^{\nu}\left(\sigma^{\prime}\right)\right}=\pi \delta_{A B} \eta^{\mu \nu} \delta\left(\sigma-\sigma^{\prime}\right) .
$$
For the open string there is a Ramond (R) fermionic sector and a Neveu-Schwarz (NS) bosonic sector, whereas for the closed string there are four fermionic sectors: $\mathrm{R}-\mathrm{R}, \mathrm{R}-\mathrm{NS}, \mathrm{NS}-\mathrm{R}$ and NS-NS sectors.
For the open string we have the modes $\alpha_{n}^{\mu}, d_{n}^{\mu}$ in the $\mathrm{R}$ sector and the modes $\alpha_{n}^{\mu}$, $b_{r}^{\mu}$ in the NS sector. For the right-movers closed string we have the modes $\alpha_{n}^{\mu}, d_{n}^{\mu}$ in the R sector and the modes $\alpha_{n}^{\mu}, b_{r}^{\mu}$ in the NS sector while for the left-movers closed string we have the modes $\tilde{\alpha}{n}^{\mu}, \tilde{d}{n}^{\mu}$ in the $\mathrm{R}$ sector and the modes $\tilde{\alpha}{n}^{\mu}, \tilde{b}{r}^{\mu}$ in the NS sector.
物理代写|弦论代写string theory代考|超引力代写supergravity|Ramond (fermionic) and Neveu–Schwarz (bosonic) open string sectors
We consider in this section the open string.
The bosonic Virasoro generator is given by
$$
\begin{aligned}
L_{m}(\tau) &=\frac{1}{\pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} T_{++} \
&=\frac{1}{\pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} \partial_{+} X^{\mu} \partial_{+} X_{\mu}+\frac{i}{2 \pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} \psi_{+}^{\mu} \partial_{+} \psi_{+\mu} \
&=L_{m}^{a}(\tau)+\frac{i}{2 \pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} \psi_{+}^{\mu} \partial_{+} \psi_{+\mu} .
\end{aligned}
$$
The first contribution $L_{m}^{\alpha}(\tau)$ was already computed. It is given by
$$
L_{m}^{\alpha}(\tau)=\frac{1}{2} \sum_{n=-\infty}^{\infty} \alpha_{-n}^{\mu}\left(\alpha_{m+n}\right)_{\mu} e^{-i m \tau} .
$$
The second contribution is given in the Ramond sector by (using the anticommutation of the fermionic degrees of freedom)
$$
\begin{aligned}
L_{m}^{d}(\tau) &=\frac{i}{2 \pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} \psi_{+}^{\mu} \partial_{+} \psi_{+\mu} \
&=\frac{1}{2} \sum_{n=-\infty}^{\infty}(n+m) d_{-n}^{\mu}\left(d_{n}+m\right){\mu} e^{-i m \tau} \ &=\frac{1}{2} \sum{n=-\infty}^{\infty}\left(n+\frac{1}{2} m\right) d_{-n}^{\mu}\left(d_{b}+m\right){\mu} e^{-i m \tau}, \mathrm{R} . \end{aligned} $$ Similarly, in the Neveu-Schwarz sector the second contribution is given by $$ \begin{aligned} L{m}^{b}(\tau) &=\frac{i}{2 \pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} \psi_{+}^{\mu} \partial_{+} \psi_{+\mu} \
&=\frac{1}{2} \sum_{r=-\infty}^{\infty}(r+m) b_{-r}^{\mu}\left(d_{n}+m\right){\mu} e^{-i m \tau} \ &=\frac{1}{2} \sum{r=-\infty}^{\infty}\left(r+\frac{1}{2} m\right) b_{-r}^{\mu}\left(d_{n}+m\right){\mu} e^{-i m \tau}, \quad \mathrm{NS} \end{aligned} $$ $r+\frac{1}{2}$ is an integer. Recall that $T=1 /\left(2 \pi \alpha^{\prime}\right)=1 /\left(\pi l^{2}\right), p^{\mu}=\alpha{0}^{\mu} / l$. We have chosen $T=1 / \pi$. Then
$$
\begin{gathered}
\alpha^{\prime} M^{2}=-\alpha^{\prime} p_{\mu} p^{\mu} \
=-L_{0}^{\alpha}(0)+\sum_{n=1} \alpha_{-n}^{\mu} \
=-L_{0}(0)+L_{0}^{d, b}(0)+\sum_{n=1} \alpha_{-n}^{\mu}\left(\alpha_{n}\right){\mu} \ =-L{0}(0)+N \
N=N^{d}+N^{\alpha}, \quad N^{d}=L_{0}^{(0)}=\sum_{n=1} n d_{-n}^{\mu}\left(d_{n}\right){\mu}, \ N^{\alpha}=\sum{n=1} \alpha_{-n}^{\mu}\left(\alpha_{n}\right){\mu}, \quad \mathrm{R} \ N=N^{b}+N^{\alpha}, \quad N^{b}=L{0}^{b}(0)=\sum_{r=1 / 2} r b_{-r}^{\mu}\left(b_{r}\right){\mu}, \ N^{\alpha}=\sum{n=1} \alpha_{-n}^{\mu}\left(b_{r}\right){\mu}, \quad \mathrm{NS} . \end{gathered} $$ Recall the classical constraints $T{++}=T_{-{-}}=J{+}=J_{-}=0$. The quantum constraints are $L_{m}(\tau)=0, F_{m}(\tau)=G_{r}(\tau)=0$. Thus the mass-shell condition will reduce to
$$
\alpha^{\prime} M^{2}=N+\text { constant. }
$$
物理代写|弦论代写STRING THEORY代考|超引力代写SUPERGRAVITY|Super-Virasoro algebra
In the bosonic string we have found that the energy-momentum tensor $T_{a \beta}$ is conserved because of spacetime translation symmetry. However, the requirement of conformal invariance led to the stronger condition that the energy-momentum tensor must vanish, viz $T_{++}=T_{–}=0 .{ }^{3}$ These equations are also derived as the equations of motion for the worldsheet metric $h_{\alpha \beta}$. The Virasoro generators $L_{m}$ are the Fourier modes of the energy-momentum tensor component $T_{++}$. They satisfy the quantum Virasoro algebra with a central extension, viz
$$
\left[L_{m}, L_{n}\right]=(m-n) L_{m+n}+\frac{D}{12} m\left(m^{2}-1\right) \delta_{m+n, 0} .
$$
The constraints $T_{++}=T_{–}=0$ become then $L_{m}=0, m=0, \pm 1, \ldots$, where $H=L_{0}$ is the Hamiltonian.
We generalize this to the RNS open superstring. We will have as before the energy-momentum tensor $T_{\alpha \beta}$ associated with global spacetime translations but now we will also have the supercurrent $J_{\alpha}$ associated with global supersymmetry. They are both conserved, viz $\partial_{\pm} T_{\mp \mp}=0, \partial_{\pm} J_{\mp}=0$. The requirement of superconformal invariance leads now to the vanishing of the energy-momentum tensor and the supercurrent, viz $T_{++}=T_{–}=J_{+}=J_{-}=0$. Alternatively, these equations can be derived as the equations of motion for the worldsheet metric $h_{\alpha \beta}$ and the gaugino field $\chi_{\alpha}$. The super-Virasoro generators consist of the bosonic Virasoro generators $L_{m}$, which are the Fourier modes of the energy-momentum tensor component $T_{++}$, and the fermionic generators $F_{m} / G_{r}$, which are the Fourier modes of the supercurrent $J_{+}$, in the Ramond/Neveu-Schwarz sectors. We have then:
- The Ramond sector: In this sector the spectrum in the Hilbert space of states will be fermionic in spacetime. The underlying degrees of freedom are the bosonic oscillators $\alpha_{n}^{\mu}$ and the $\mathrm{R}$ fermionic oscillators $d_{n}^{\mu}$ where $n$ is an integer. The bosonic Virasoro generators $L_{m}$ will be given by the bosonic string contribution $+\mathrm{a}$ contribution coming from the $\mathrm{R}$ fermionic oscillators as follows (including now normal ordering explicitly) ${ }^{4}$
$$
\begin{gathered}
L_{m}=L_{m}^{\alpha}+L_{m}^{d} \
L_{m}^{\alpha}=\frac{1}{2} \sum_{n=-\infty}^{\infty}: \alpha_{-n}^{\mu}\left(\alpha_{m+n}\right){\mu}: \ L{m}^{d}=\frac{1}{2} \sum_{n=-\infty}^{\infty}\left(n+\frac{1}{2} m\right): d_{-n}^{\mu}\left(d_{n+m}\right)_{\mu}:
\end{gathered}
$$
弦论超引力代写
物理代写|弦论代写STRING THEORY代考|超引力代写SUPERGRAVITY|COMMUTATION RELATIONS
玻色子坐标的量化Xμ发现由对易关系给出
[∂τXμ(σ),Xν(σ′)]=−一世圆周率d(σ−σ′)这μν.
这些导致交换关系
$$
\left[\partial_{\tau} X^{\mu}(\sigma), X^{\nu}\left(\sigma^{\prime}\right)\right]=-i \pi \delta\left(\sigma-\sigma^{\prime}\right) \eta^{\mu \nu} .
$$
These lead to the commutation relations
$$
\begin{aligned}
& {\left[\alpha_{n}^{\mu}, \alpha_{m}^{\nu}\right]=n \delta_{n+m, 0} \eta^{\mu \nu}, \quad \text { open string. } } \
{\left[\alpha_{n}^{\mu}, \alpha_{m}^{\nu}\right] } &=\left[\tilde{\alpha}{n}^{\mu}, \widetilde{\alpha}{m}^{\nu}\right] \
&=n \delta_{n+m, 0} \eta^{\mu \nu}, \quad\left[\alpha_{n}^{\mu}, \tilde{\alpha}{m}^{\nu}\right]=0, \quad \text { closed string. } \end{aligned} $$ Similarly the quantization of the fermionic coordinates $\psi{A}^{\mu}$ is found to be given by the anticommutation relations
$$
\left{\psi_{A}^{\mu}(\sigma), \psi_{B}^{\nu}\left(\sigma^{\prime}\right)\right}=\pi \delta_{A B} \eta^{\mu \nu} \delta\left(\sigma-\sigma^{\prime}\right) .
$$
对于开放字符串，我们有模式一种nμ,dnμ在里面R部门和模式一种nμ,brμ在NS领域。对于右移闭合字符串，我们有模式一种nμ,dnμ在 R 部门和模式一种nμ,brμ在 NS 扇区中，而对于左移闭合字符串，我们有模式 $\tilde{\alpha} {n}^{\mu}, \tilde{d} {n}^{\mu}一世n吨H和\mathrm{R}s和C吨这r一种nd吨H和米这d和sNS 扇区中的\tilde{\alpha} {n}^{\mu}, \tilde{b} {r}^{\mu}$。
物理代写|弦论代写STRING THEORY代考|超引力代写SUPERGRAVITY|RAMONDF和r米一世这n一世C和 NEVEU-BLACKb这s这n一世C打开字符串扇区
我们在本节中考虑开放字符串。
玻色子 Virasoro 发生器由下式给出
大号米(τ)=1圆周率∫−圆周率圆周率dσ和一世米σ吨++ =1圆周率∫−圆周率圆周率dσ和一世米σ∂+Xμ∂+Xμ+一世2圆周率∫−圆周率圆周率dσ和一世米σψ+μ∂+ψ+μ =大号米一种(τ)+一世2圆周率∫−圆周率圆周率dσ和一世米σψ+μ∂+ψ+μ.
第一个贡献大号米一种(τ)已经计算过了。它是由
大号米一种(τ)=12∑n=−∞∞一种−nμ(一种米+n)μ和−一世米τ.
第二个贡献是在拉蒙德部门由你s一世nG吨H和一种n吨一世C这米米你吨一种吨一世这n这F吨H和F和r米一世这n一世Cd和Gr和和s这FFr和和d这米
$$
\begin{aligned}
L_{m}^{d}(\tau) &=\frac{i}{2 \pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} \psi_{+}^{\mu} \partial_{+} \psi_{+\mu} \
&=\frac{1}{2} \sum_{n=-\infty}^{\infty}(n+m) d_{-n}^{\mu}\left(d_{n}+m\right){\mu} e^{-i m \tau} \ &=\frac{1}{2} \sum{n=-\infty}^{\infty}\left(n+\frac{1}{2} m\right) d_{-n}^{\mu}\left(d_{b}+m\right){\mu} e^{-i m \tau}, \mathrm{R} . \end{aligned} $$ Similarly, in the Neveu-Schwarz sector the second contribution is given by $$ \begin{aligned} L{m}^{b}(\tau) &=\frac{i}{2 \pi} \int_{-\pi}^{\pi} d \sigma e^{i m \sigma} \psi_{+}^{\mu} \partial_{+} \psi_{+\mu} \
&=\frac{1}{2} \sum_{r=-\infty}^{\infty}(r+m) b_{-r}^{\mu}\left(d_{n}+m\right){\mu} e^{-i m \tau} \ &=\frac{1}{2} \sum{r=-\infty}^{\infty}\left(r+\frac{1}{2} m\right) b_{-r}^{\mu}\left(d_{n}+m\right){\mu} e^{-i m \tau}, \quad \mathrm{NS} \end{aligned} $$ $r+\frac{1}{2}$ is an integer. Recall that $T=1 /\left(2 \pi \alpha^{\prime}\right)=1 /\left(\pi l^{2}\right), p^{\mu}=\alpha{0}^{\mu} / l$. We have chosen $T=1 / \pi$. Then
$$
\begin{gathered}
\alpha^{\prime} M^{2}=-\alpha^{\prime} p_{\mu} p^{\mu} \
=-L_{0}^{\alpha}(0)+\sum_{n=1} \alpha_{-n}^{\mu} \
=-L_{0}(0)+L_{0}^{d, b}(0)+\sum_{n=1} \alpha_{-n}^{\mu}\left(\alpha_{n}\right){\mu} \ =-L{0}(0)+N \
N=N^{d}+N^{\alpha}, \quad N^{d}=L_{0}^{(0)}=\sum_{n=1} n d_{-n}^{\mu}\left(d_{n}\right){\mu}, \ N^{\alpha}=\sum{n=1} \alpha_{-n}^{\mu}\left(\alpha_{n}\right){\mu}, \quad \mathrm{R} \ N=N^{b}+N^{\alpha}, \quad N^{b}=L{0}^{b}(0)=\sum_{r=1 / 2} r b_{-r}^{\mu}\left(b_{r}\right){\mu}, \ N^{\alpha}=\sum{n=1} \alpha_{-n}^{\mu}\left(b_{r}\right){\mu}, \quad \mathrm{NS} . \end{gathered} $$ Recall the classical constraints $T{++}=T_{-{-}}=J{+}=J_{-}=0$. The quantum constraints are $L_{m}(\tau)=0, F_{m}(\tau)=G_{r}(\tau)=0$. Thus the mass-shell condition will reduce to
$$
\alpha^{\
物理代写|弦论代写STRING THEORY代考|超引力代写SUPERGRAVITY|SUPER-VIRASORO ALGEBRA
在玻色子弦中，我们发现能量-动量张量吨一种b由于时空平移对称性而守恒。然而，共形不变性的要求导致能量-动量张量必须消失的更强条件，即吨++=吨–=0.3这些方程也被导出为世界表度量的运动方程H一种b. Virasoro 发电机大号米是能量-动量张量分量的傅里叶模式吨++. 它们满足具有中心扩展的量子 Virasoro 代数，即
[大号米,大号n]=(米−n)大号米+n+D12米(米2−1)d米+n,0.
约束吨++=吨–=0成为那时大号米=0,米=0,±1,…， 在哪里H=大号0是哈密顿量。
我们将其推广到 RNS 开放超弦。我们将像以前一样拥有能量-动量张量吨一种b与全球时空转换相关，但现在我们也将拥有超电流Ĵ一种与全局超对称有关。它们都是保守的，即∂±吨∓∓=0,∂±Ĵ∓=0. 超共形不变性的要求现在导致能量-动量张量和超流的消失，即吨++=吨–=Ĵ+=Ĵ−=0. 或者，这些方程可以导出为世界表度量的运动方程H一种b和高吉诺领域χ一种. 超级 Virasoro 发生器由玻色 Virasoro 发生器组成大号米，它们是能量-动量张量分量的傅里叶模式吨++, 和费米子发生器F米/Gr，它们是超电流的傅里叶模式Ĵ+，在 Ramond/Neveu-Schwarz 部门。那么我们有：
- 拉蒙德扇区：在这个扇区中，状态希尔伯特空间中的光谱在时空中将是费米子的。基本自由度是玻色子振荡器一种nμ和R费米子振荡器dnμ在哪里n是一个整数。玻色子 Virasoro 发生器大号米将由玻色子弦贡献给出+一种贡献来自R费米子振荡器如下一世nC一世你d一世nGn这在n这r米一种一世这rd和r一世nG和Xp一世一世C一世吨一世是 4
$$
\begin{聚集}
L_{m}=L_{m}^{\alpha}+L_{m}^{d} \
L_{m}^{\alpha}=\frac{1}{2} \ sum_{n=-\infty}^{\infty}: \alpha_{-n}^{\mu}\left\alpha_{m+n}\右\alpha_{m+n}\右{\mu}: \L {m}^{d}=\frac{1}{2} \sum_{n=-\infty}^{\infty}\leftn+\frac{1}{2} m\rightn+\frac{1}{2} m\right: d_{-n}^{\mu}\leftd_{n+m}\右d_{n+m}\右_{\mu}:
\end{聚集}
$$
物理代写|弦论代写string theory代考|超引力代写supergravity 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。
