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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子力学代写quantum mechanics代考|Example of Intrinsic, Observed and Coordinate

The electromagnetic theory gives us the opportunity to illustrate our discussion concerning the intrinsic, observed and coordinate languages (see the above Sect. 1.2.6).
Most topics discussed in the present book are presented in an analogous way.
(1a) The electromagnetic field can be defined, in intrinsic way, as a scaled spacetime 2-form $F: \boldsymbol{E} \rightarrow\left(\mathbb{L}^{1 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes \Lambda^2 T^* \boldsymbol{E}$ (see Definition 5.1.1).

Actually, this definition holds both in the galilean and einsteinian frameworks, because it involves only the spacetime manifold $\boldsymbol{E}$, without reference to any further additional geometric structure.
(1b) In any spacetime chart, the coordinate expression of the electromagnetic field is $F=2 F_{0 j} d^0 \wedge d^j+F_{i j} d^i \wedge d^j$.

With reference to suitable spacetime charts, this expression holds both in the galilean and einsteinian frameworks.
(1c) In the galilean framework, an observer is defined to be a normalised scaled spacetime vector field $д[o]: \boldsymbol{E} \rightarrow \mathbb{T}^* \otimes T \boldsymbol{E}$, with coordinate expression $д[o]=$ $u^0 \otimes\left(\partial_0+o_0^i \partial_i\right),($ see Definition $2.7 .1$ and Proposition 2.7.3).

We observe that, in the einsteinian framework, the observers can be defined in a rather analogous way. But differences between the galilean and the einsteinian cases arise due to the fact that in the two cases, respectively, the time fibring and the lorentzian metric are involved.

Then, in the galilean framework, the magnetic vector field and the observed magnetic 1-form are defined as the scaled spacetime sections (see Definition 5.2.1)

$$\begin{array}{ll} \vec{B} & :=\frac{c}{2} i_{\breve{F}} \bar{\eta}: \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{-3 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes V \boldsymbol{E} \ B[o]: & :=\theta[o]\lrcorner \vec{B}: \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{1 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes T^* \boldsymbol{E} \end{array}$$
Moreover, in the galilean framework, the observed electric I-form and the observed electric vector field are defined as the scaled spacetime sections (see Definition 5.3.1)
\begin{aligned} &E[o]:=-\not[o]\lrcorner F: \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{1 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes T^* \boldsymbol{E}, \ &\vec{E}[o]:=g^{\Perp}(\check{E}[o]): \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{-3 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes V \boldsymbol{E} . \end{aligned}

## 物理代写|量子力学代写quantum mechanics代考|Joined Spacetime Connection

We “join”, by means of a covariant minimal coupling, the gravitational field and the electromagnetic field $K^{\natural}: T \boldsymbol{E} \rightarrow T^* \boldsymbol{E} \otimes T T \boldsymbol{E}$ and $F: \boldsymbol{E} \rightarrow\left(\mathbb{L}^{1 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes$ $\Lambda^2 T^* \boldsymbol{E}$ into a “joined spacetime connection” (see Theorem 6.3.1)
$$K \equiv K^{\natural}+K^e:=K^{\natural}-\frac{1}{2} \mathrm{k}(d t \otimes \hat{F}+\hat{F} \otimes d t): T \boldsymbol{E} \rightarrow T^* \boldsymbol{E} \otimes T T \boldsymbol{E},$$
with coordinate expression
\begin{aligned} &K_0{ }^i{ }_0=K^{\natural}{ }_0{ }_0{ }_0-k_0 F_0{ }^i, \ &K_0{ }_j{ }^i=K_0^i{ }_j=K_0^{\natural}{ }_j{ }_j-\frac{1}{2} \mathrm{k}_0 F_j^i=K_j^{\natural}{ }_j^i-\frac{1}{2} \mathrm{k}_0 F_j^i, \ &K_h{ }^i k=K^{\natural} h^i{ }^i . \end{aligned}
In the present book, we deal with two specifications of the above coupling constant $k \in\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{3 / 2} \otimes \mathbb{M}^{-1 / 2}\right) \otimes \mathbb{R}$.
The most relevant case is provided by the “electromagnetic joining scale”
$$k:=\frac{q}{m} \in\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{3 / 2} \otimes \mathbb{M}^{-1 / 2}\right) \otimes \mathbb{R},$$
which is systematically used for a concise formulation of Classical and Quantum Mechanics, with reference to a particle of mass $m$ and change $q$.
A further, minor case is provided by the “gravitational joining scale”
$$k:-\sqrt{r} \in \mathbb{T}^{-1} \otimes \mathbb{L}^{3 / 2} \otimes \mathbb{M}^{-1 / 2},$$
which is used for the formulation of “Galilei-Einstein equation”.

# 量子力学代考

## 物理代写|量子力学代写quantum mechanics代考|Example of Intrinsic, Observed and Coordinate

(1a) 电磁场可以以固有的方式定义为缩放的时空 2-形式 $F: \boldsymbol{E} \rightarrow\left(\mathbb{L}^{1 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes \Lambda^2 T^* \boldsymbol{E}$ (见定义 5.1.1)。

(1b) 在任何时空图中，电磁场的坐标表达式为 $F=2 F_{0 j} d^0 \wedge d^j+F_{i j} d^i \wedge d^j$.

(1c) 在伽利略框架中，观察者被定义为归一化的缩放时空矢量场 $d[o]: \boldsymbol{E} \rightarrow \mathbb{T}^* \otimes T \boldsymbol{E}$, 带坐标表达式 $d[o]=u^0 \otimes\left(\partial_0+o_0^i \partial_i\right)$, (见定义 $2.7 .1$ 和提案 2.7.3)。

$$\left.\vec{B}:=\frac{c}{2} i_{\bar{F}} \bar{\eta}: \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{-3 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes V \boldsymbol{E} B[o]: \quad:=\theta[o]\right\lrcorner \vec{B}: \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{1 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes T^* \boldsymbol{E}$$

$$E[o]:=-\Lambda o]\lrcorner F: \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{1 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes T^* \boldsymbol{E}, \quad \vec{E}[o]:=g^{\backslash \operatorname{Perp}}(\check{E}[o]): \boldsymbol{E} \rightarrow\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{-3 / 2} \otimes \mathbb{M}^{1 / 2}\right) \otimes V \boldsymbol{E} .$$

## 物理代写|量子力学代写quantum mechanics代考|Joined Spacetime Connection

$$K \equiv K^{\natural}+K^e:=K^{\natural}-\frac{1}{2} \mathrm{k}(d t \otimes \hat{F}+\hat{F} \otimes d t): T \boldsymbol{E} \rightarrow T^* \boldsymbol{E} \otimes T T \boldsymbol{E},$$
$$K_0{ }0^i=K^{\natural}{ }{000}-k_0 F_0{ }^i, \quad K_{0 j}{ }^i=K_{0 j}^i=K_{0 j j}^{\natural}-\frac{1}{2} \mathrm{k}0 F_j^i=K{j j}^{\natural i}-\frac{1}{2} \mathrm{k}_0 F_j^i, K_h{ }^i k=K^{\natural} h^{i i} .$$

$$k:=\frac{q}{m} \in\left(\mathbb{T}^{-1} \otimes \mathbb{L}^{3 / 2} \otimes \mathbb{M}^{-1 / 2}\right) \otimes \mathbb{R}$$

“引力连接尺度“提供了另一个较小的情况
$$k:-\sqrt{r} \in \mathbb{T}^{-1} \otimes \mathbb{L}^{3 / 2} \otimes \mathbb{M}^{-1 / 2},$$

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