REVTEX 3.0 Released November 10, 1992

APPENDIX A: CHARACTER SET LISTING

This appendix provides tables which show all of the special characters and mathematical symbols that are available within REVTEX. Some of these symbols require the AMSFonts to be available.

REVTEX version 3.0 supports an extensive set of symbols, alphabets, and special fonts. Their availability does not relieve an author (editor) of considering whether a chosen notation or symbol will convey the intended meaning, and whether there is a more conventional alternative. As always, for the benefit of the reader, notation should be clear, as simple as possible, and consistent with standard usage. Nonstandard symbols should only be used if necessary; their meaning should be explained in the paper at the first occurrence.

Editorial policy on this issue may vary from journal to journal. Check recent issues of a given journal and/or query the editor. APS authors may also consult the journal’s “Information for Contributors” as well as the Physical Review Style and Notation Guide. In preparing an accepted paper for publication, the editor may suggest (require) the use of alternative notation.

1. LaTeX notations

a. Standard LaTeX symbols

The following tables show the standard symbols for L^{A}TEX users.

TABLE I. Text accents with letter a.

à \`{a}  á \'{a}  â \^{a}  ä \"{a}
ã \~{a}  ā \={a}  ȧ \.{a}  ă \u{a}
ǎ \v{a}  a̋ \H{a}  aa \t{aa}  a̧ \c{a}
a. \d{a}        ā \b{a}

TABLE II. Math accents with letter a.

â \hat{a}     ǎ \check{a}   ȧ \dot{a}     ä \ddot{a}
ă \breve{a}   ã \tilde{a}   à \grave{a}   á \acute{a}
ā \bar{a}     a⃗ \vec{a}

TABLE III. Special symbols; any mode.

† \dag  § \S              \begin{matrix}c \\ ◯ \end{matrix} \copyright
‡ \ddag  ¶ \P  £ \pounds

TABLE IV. Other special (foreign) symbols; text mode.

å \aa  Å \AA  æ \ae  Æ \AE
ø \o  Ø \O  œ \oe  Œ \OE
ł \l  Ł \L  ¿ ?`  ¡ !`
ß \ss

TABLE V. Greek letters; used in math mode.

Lowercase

α \alpha  β \beta  γ \gamma  δ \delta
ϵ \epsilon ε \varepsilon ζ \zeta  η \eta
θ \theta  ϑ \vartheta  ι \iota  κ \kappa
λ \lambda μ \mu  ν \nu  ξ \xi
o o  π \pi  ϖ \varpi  ρ \rho
ϱ \varrho σ \sigma  ς \varsigma τ \tau
υ \upsilon ϕ \phi  φ \varphi  χ \chi
ψ \psi  ω \omega

Uppercase

Γ \Gamma  Δ \Delta  Θ \Theta  Λ \Lambda
Ξ \Xi  Π \Pi  Σ \Sigma  Υ \Upsilon
Φ \Phi  Ψ \Psi  Ω \Omega

TABLE VI. Binary operation symbols; used in math mode.

± \pm  ∓ \mp  × \times ÷ \div
∗ \ast  ⋆ \star  ∘ \circ • \bullet
∩ \cap  ∪ \cup  ⊎ \uplus · \cdot
⊓ \sqcap  ⊔ \sqcup ∨ \vee  ∧ \wedge
⊕ \oplus  ⊖ \ominus ⊗ \otimes ⊘ \oslash
△ \bigtriangleup ⊙ \odot  ⊲ \lhd  † \dagger
▽ \bigtriangledown ◯ \bigcirc ⊳ \rhd  ‡ \ddagger
◁ \triangleleft  ⋄ \diamond ⊴ \unlhd \ \setminus
▷ \triangleright ≀ \wr  ⊵ \unrhd ⨿ \amalg

TABLE VII. Relation symbols; used in math mode.

≤ \leq  ≥ \geq  ≪ \ll  ≫ \gg
≡ \equiv  ≍ \asymp  ≠ \neq        ≐ \doteq
⊂ \subset ⊃ \supset ⊆ \subseteq ⊇ \supseteq
⊏ \sqsubset ⊐ \sqsupset ⊑ \sqsubseteq ⊒ \sqsupseteq
⊧ \models ⊥ \perp  | \mid  ∥ \parallel
≺ \prec  ≻ \succ  ⪯ \preceq  ⪰ \succeq
∼ \sim  ≃ \simeq  ≈ \approx     ≅ \cong
▷◁ \bowtie ⋈ \Join  ⌣ \smile  ⌢ \frown
∈ \in  ∋ \ni  ⊢ \vdash  ⊣ \dashv
∝ \propto

A-1 \begin{matrix}c \\ ◯ \end{matrix} 1992 American Physical Society Optical Society of America American Institute of Physics

Negated relations can sometimes be constructed with \not. For example,

If $x \not< y$ then $x \not\leq z$.

gives

If x ≮ y then x ≰ z.

The AMSFonts have many negated relations already constructed. See Appendix A 2.

TABLE VIII. Arrow symbols; used in math mode.

← \leftarrow  → \rightarrow
⟵ \longleftarrow  ⟶ \longrightarrow
⇐ \Leftarrow  ⇒ \Rightarrow
⟸ \Longleftarrow  ⟹ \Longrightarrow
↩ \hookleftarrow  ↪ \hookrightarrow
↼ \leftharpoonup  ⇀ \rightharpoonup
↽ \leftharpoondown  ⇁ \rightharpoondown
⇀ ↽ \rightleftharpoons  ⇝ \leadsto
↔ \leftrightarrow  ⟷ \longleftrightarrow
⇔ \Leftrightarrow  ⟺ \Longleftrightarrow
↦ \mapsto  ⟼ \longmapsto
↑ \uparrow
↓ \downarrow
⇑ \Uparrow
⇓ \Downarrow
↕ \updownarrow
⇕ \Updownarrow
↗ \nearrow
↘ \searrow
↙ \swarrow
↖ \nwarrow

TABLE IX. Miscellaneous symbols; used in math mode.

♭ \flat  ♮ \natural ♯ \sharp  ′ \prime
\ \backslash  ∀ \forall ∞ \infty  ∃ \exists
∅ \emptyset  □ \Box  ∇ \nabla  ¬ \neg
◇ \Diamond  √ \surd  △ \triangle ∥ \|
♣ \clubsuit  ℵ \aleph  ℘ \wp  ⊤ \top
♢ \diamondsuit ℜ \Re  ℓ \ell  ⊥ \bot
♡ \heartsuit ℑ \Im  ı \imath  ∂ \partial
♠ \spadesuit  h̄ \hbar  ȷ \jmath     ^{}\angle
℧ \mho

TABLE X. Log-like functions; used in math mode.

\arccos    \arcsin    \arctan    \arg     \cos
\cosh      \cot       \coth      \csc     \deg
\det       \dim       \exp       \gcd     \hom
\inf       \ker       \lg        \lim     \liminf
\limsup    \ln        \log       \max     \min
\Pr        \sec       \sin       \sinh    \sup
\tan       \tanh

TABLE XI. Delimiters; used in math mode.

( (  ) )  / /
[ [  ] ]  \ \backslash
{ \{  } \}  | |
⟨ \langle  ⟩ \rangle  ∥ \|
↑ \uparrow  ⇑ \Uparrow  ⌊ \lfloor
↓ \downarrow  ⇓ \Downarrow  ⌋ \rfloor
↕ \updownarrow  ⇕ \Updownarrow  ⌈ \lceil
                                        ⌉ \rceil

TABLE XII. Miscellaneous symbols; used in math mode.

∑ ∑ \sum  ∏ ∏ \prod  ∐ ∐ \coprod
 ∫ ∫ \int  ∮ ∮ \oint  ⨄ ⨄ \biguplus
 ⋂ ⋂ \bigcap ⋃ ⋃ \bigcup  ⨆ ⨆ \bigsqcup
⨀ ⨀ \bigodot ⨂ ⨂ \bigotimes ⨁ ⨁ \bigoplus
 ⋁ ⋁ \bigvee ⋀ ⋀ \bigwedge

b. Standard LaTeX typefaces

You can access a pair of special typefaces in L^{A}TEX. You can switch to script (calligraphic) letters by using

the \cal command (note the L):

{\cal L}_{\text{int}} = e F^{3}_{\pi} r^{2}
  B^{0}(r,t) \epsilon \sin(\Omega t)
  \exp(\eta t),

gives

L_{int} = eF_{π}^{3}r^{2}B^{0}(r, t)ϵ sin(Ωt) exp(ηt),

Only uppercase letters are available in the \cal font.

A-2

You can switch to sans serif letters by using the \sf command (note the M):

R({\cal Q}-{\cal Q}_{0})
=R_{0} \exp\left(-\case1/2\Delta {\cal Q}
\cdot{\sf M}\cdot\Delta{\cal Q}\right).
\label{eq:rdef}

gives

R(Q − Q_{0}) = R_{0} exp (−\frac{1}{2}ΔQ · M · ΔQ) .

Both uppercase and lowercase letters are available with

\sf.

c. Other notations

The \overline command puts a horizontal line above its argument in math mode:

$\overline{x}+\overline{y}$

gives

\overline{x} + \overline{y}

There is an analogous \underline command that works in text or math mode:

The equation \underline{is} $\underline{x+y}$.

gives

The equation \underline{is} \underline{x + y}.

Horizontal braces are put above or below an expression

with the \overbrace and \underbrace commands:
$\underbrace{a_{1} + \overbrace{a_{2}+a_{3}}
+ a_{4}}$

gives

\underbrace{a_{1} + \overbrace{a_{2} + a_{3}} +a_{4}}

and in displayed math, a subscript or a superscript puts a label on the brace:

$\underbrace{a_{1} +
\overbrace{a_{2}+\cdots+a_{n-1}}^{n-2}
+ a_{n}}_{n}$

gives

\underbrace{a_{1} + \overbrace{a_{2} + ⋯ + a_{n−1}}^{n−2} +a_{n}}_{n}

Wide versions of the \hat and \tilde commands are available. They are called \widehat and \widetilde, respectively. Here is an example:

$\widehat{a} + \widehat{ab}
+ \widehat{abc} + \widehat{abcd}$

gives

â + âb + âbc + âbcd

2. AMSFonts notations

The AMSFonts are fonts that were developed by the American Mathematical Society and are now made available free of charge by the AMS. The METAFONT source files for these fonts are freely available, as are precompiled .pk files. There are two style options that can be used to access the AMSFonts: amsfonts and amssymb. These style options are explained in The appropriate societyspecific documentation. Not distributed with REVTEX are the files amsfonts.sty and amssymb.sty of the AMS-L^{A}TEX distribution. These files are called in by REVTEX, when the NFSS is in effect, to give you access to the AMSFonts; under the OFSS REVTEX itself will do the work necessary to allow access.

a. Using the amsfonts option

The amsfonts style option will give you access to the \frak and \Bbb fonts and will also use the extra Computer Modern fonts from the AMS in order to provide better access to bold math characters at smaller sizes and in super- and subscripts.

AMSFonts typefaces. With the AMSFonts installed and in use through either the amsfonts or amssymb style option, the \frak and \Bbb commands are available. \frak switches to the AMS Fraktur font, while \Bbb switches to the so-called “Blackboard Bold” font. Only uppercase letters are available in Blackboard Bold, and there is no bold version of the font. Fraktur has both uppercase and lowercase letters and will become bold in a bbox.

You do not have the amsfonts or amssymb option selected, therefore the characters in the AMSFonts will not be printed using \frak and

                     \Bbb.

b. Using the amssymb option

The amssymb style option gives all the font capabilities of the amsfonts option. It also defines names for many extra symbols that are present in the AMSFonts. The names are the same as those the AMS uses. These symbols and their names are shown below, if you have the AMSFonts installed and the amssymb option selected.

You do not have the amssymb option selected, therefore the characters in the AMSFonts will

not be printed.

A-3

3. REVTEX notations

An openface one is available. It does not change size in superscripts. Here is an example: $\openone$ gives 11. \openone is a fragile command and must be immediately preceded by \protect when used in section headings and captions.

Bold large bracketing is also available. The normal commands \Biggl,\Bigl,…, when used with an extra “b” on the end of the command, come out bold:

\[
\Biggl(\biggl(\Bigl(\bigl(
(x)
\bigr)\Bigr)\biggr)\Biggr)
\]

gives

(((((x)))))

while

\[
\Bigglb(\bigglb(\Biglb(\biglb(
(x)
\bigrb)\Bigrb)\biggrb)\Biggrb)
\]

gives

( ( (( ( (( ( (((((x))))) ) )) ) )) ) )

The commands \lesssim,\gtrsim give the output < ∼, > ∼, even without the amssymb style option. (The commands \alt,\agt, respectively, may also be used.) These commands will be fragile if you are not using the amssymb option.

Some extra diacritics have been provided. They scale correctly in superscripts. Some examples fol-

low. $\tensor{x}$ gives x^{↔}. $\overstar{x}$ gives
x^{∗}. $\overdots{x}$ gives x^{···}. $\overcirc{x}$ gives x^{∘}.
$\loarrow{x}$ gives x^{←}. $\roarrow{x}$ gives x^{→}. These

commands all work correctly in superscripts.

\slantfrac{#1}{#2} produces a slanted fraction in math mode: ^{1}/_{2}. This command should not be used in files destined to be submitted to the APS (normal upright fractions will be produced).

\corresponds produces the symbol =^{△} math mode, \precsim produces ≺_{∼} in math mode, and \succsim produces ≻_{∼} in math mode. The AMSFonts will be used for these symbols if you have them, but are not necessary.

\lambdabar produces “lambda-bar” in math mode: λ.

A-4

APPENDIX B: COMMAND LIST

In the following pages are brief descriptions of some necessary commands. Those commands that are unique to REVTEX are so noted with (R). Please consult the L^{A}TEX User’s Guide & Reference Manual if you have further questions regarding L^{A}TEX commands.

If commands require arguments, they are so noted with #1, #2, etc. The commands are in order of their probable occurrence in a file.

\documentstyle[#1]{revtex} Will allow for proper formatting of paper. Selecting a society style option (either osa or aps) is mandatory. Use [manuscript,osa] for #1 if manuscript style is desired for the OSA macros, and use [osa] for #1 if galley style is desired for the OSA macros. Use [preprint,aps] for #1 if preprint style is desired for the APS macros, and use [aps] for #1 if galley style is desired for the APS macros. The preprint and manuscript styles are similar ideas. The author will also need to add a journal option. Consult the society-specific documentation for the relevant options. To number equations by section, use the eqsecnum option.

\tighten Preprint style outputs a double-spaced manuscript. When used in preprint style, this command reverts to single spacing to save paper. Has no effect in galley style. Use before \begin{document}. You can also use the tighten style option to get single-spaced preprint output for the whole paper. (R)

\begin{document}  Begins the body of the REVTEX document.

\preprint{#1} When used as the first command of a document, places #1 at the top right corner of the first page in preprint style. Used for site-specific preprint numbers. (R)

\draft  Omission of this command will cause printing of PACS numbers to be stifled. (R)
\title{#1}                             #1 is the title of the paper. The title should be broken with the \\ command.
\author{#1}                            #1 represents a list of authors. Use \\ to force linebreaks.

\address{#1} #1 represents an author’s address (institution). The address should be broken with \\ if necessary. (R)

\date{#1} #1 represents the date of receipt at the Editorial Offices. This date will be inserted at the production site.

\maketitle  Prints the material contained in the \title{#1}, \author{#1}, \address{#1}

and \date{#1} commands.

\begin{abstract},
\end{abstract},

Signals the beginning or end of the abstract.

\pacs{#1} #1 represents valid PACS numbers. This command should be used after the abstract, even if #1 is empty. Use the \draft command to have #1 printed. (R)

\narrowtext For galley style, will set all text that follows into a 3.4-in. column. Does not affect preprint output. (R)

\mediumtext For galley style, will set figure captions and tables 5.5-in. wide. Does not affect preprint output. (R)

\widetext For galley style, will set all text that follows into a 7-in.-wide column. Does not affect preprint output. (R)

\section{#1} #1 represents a primary heading. Fragile commands should be preceded by

\protect.

\subsection{#1} #1 represents a secondary heading. Fragile commands should be preceded by

\protect.

\subsubsection{#1} #1 represents a third-level heading. Fragile commands should be preceded by

\protect.

\paragraph{#1} #1 represents a fourth-level heading. Fragile commands should be preceded by

\protect.

B-1 \begin{matrix}c \\ ◯ \end{matrix} 1992 American Physical Society Optical Society of America American Institute of Physics

\cite{#1} Sets a reference or byline footnote citation. #1 represents a list of reference tags used with \bibitem{#1}. Lists of consecutive numbers will be collapsed; e.g., [1,2,3] will become [1–3]. The style of citation in output will depend on the society and/or journal option selected. Fragile.

\onlinecite{#1} Sets a reference citation just like \cite{#1} does, except that it places the citation on-line in styles where the citations are usually superscripts. Fragile. (R)

\case{#1}{#2} Sets textstyle (smaller) fractions in displayed equations. #1 is the numerator, #2 is denominator. An optional / may be added between {#1} and {#2}. (R)

\openone  Produces an openface one (11). Fragile. (R)
\precsim,\succsim  Produce the signs ≺_{∼} , ≻_{∼} , respectively, in math mode.

\lesssim,\gtrsim Produce “approximately less than” and “approximately greater than” signs (< ∼, > ∼), respectively, in math mode. Fragile.

\tensor{#1}  Gives double-headed overarrow in math mode: $\tensor{x}$ gives x^{↔}. (R)
\loarrow{#1}  Gives left-going overarrow in math mode: $\loarrow{x}$ gives x^{←}. (R)

\roarrow{#1} Gives right-going overarrow in math mode to match \loarrow{#1}:

                                       $\roarrow{x}$ gives x^{→}. (R)

\overstar{#1}  Gives overstar in math mode: $\overstar{x}$ gives x^{∗}. (R)
\overcirc{#1}  Gives overcircle in math mode: $\overcirc{x}$ gives x^{∘}. (R)
\biglb(, etc.  Commands to produce large bold bracketing. (R)
\corresponds  Produces “corresponds” sign in math mode: =^{△}.

\slantfrac{#1}{#2} Produces a slanted fraction in math mode: ^{1}/_{2}. Should not be used for APS files. (R)

\lambdabar  Produces “lambda-bar” in math mode: λ. (R)

\FL Sets the displayed equation that follows flush left with the margin. Only works in galley style. (R)

\FR Sets the displayed equation that follows flush right. Only works in galley style. (R)

\[,\]  Signals beginning or end of unnumbered displayed equation.
\begin{equation},\end{equation}  Signals beginning or end of single-line displayed equation.
\begin{eqnarray},\end{eqnarray}  Signals beginning or end of multiline displayed equation.
\nonumber  Suppresses the numbering of a single line in a eqnarray environment.

\eqnum{#1} Uses #1 as the number for an equation or for a single line of an eqnarray. The number can be cross-referenced with \ref{#1} if \label{#1} is used right after \eqnum{#1}. Numbers set with \eqnum{#1} are completely independent of the automatic numbering. (R)

\begin{quasitable},\end{quasitable}  Environment to produce tables in text. See apssamp.tex for an example. (R)

\label{#1} #1 represents the tag. This command appears in displayed equations that need cross-referencing, all tables, and all figure captions. Also used following section headings that need cross-referencing.

\ref{#1} #1 represents the tag. This command appears in text wherever sections, equations, tables, or figures are cited. Fragile.

\acknowledgments  Sets a section heading for the acknowledgment section.

\appendix After using this command, all \section{#1} commands will set #1 as an appendix heading. \section*{#1} will set #1 as an appendix heading without a letter (A, B, etc.) and should be used when there is only one appendix.

\begin{references},\end{references} Signals beginning or end of reference section. The normal L^{A}TEX thebibliography environment can also be used. (R)

\bibitem[#1]{#2} Sets a reference in the reference section. #1 represents an optional, authorspecified reference symbol. This is used for byline endnotes that are not numbered (e.g., those in Physical Review). #2 represents the reference tag.

\begin{figure}  Begins the environment for the figure caption.

B-2

\caption{#1} #1 represents the text of the caption. Fragile commands must be preceded by

                                       \protect.

\label{#2}                             #2 represents the figure caption tag.
\end{figure}  Ends the environment for the figure caption.
\begin{table}  Signals the beginning of a table.

\squeezetable Used immediately after \begin{table}, shrinks tables that would not otherwise fit. (R)

\caption{#1} Sets the table caption. #1 represents the text of the caption. Fragile commands must be preceded by \protect.

\begin{tabular}{#1} Signals the beginning of the tabular material. #1 represents formatting commands for the columns.

\hline Sets a horizontal rule, separating column headings from data. \tableline may also be used.

\end{tabular}  Signals end of tabular material.
\end{table}  Signals the end of a table.
\end{document}  Ends the body of the REVTEX document.

B-3