Cfxtrjtrk

It sounds like very poor typography, but I am simply looking to shift a wrapfig picture up, but in particular so it would ever so slightly go above the start of the paragraph and into the subsection line. See the attached picture below.

I provide an MWE for the picture and surrounding text (I have simply copied a load of bits from my preamble of my larger document! Apologies for the useless parts in there!).
I expect nothing in my preamble will interrupt this. I have tried putting vspace in both the wrap figure, the tikzpicture and before the entire figure in braces. Even with the abnormal vspace{-25cm}, it seems to only take the picture up to the very start of the paragraph and section - I want to slightly break this bounding box. Any suggestions would be welcomed.

documentclass[12pt,a4paper,twoside]{report}

usepackage{graphicx}

usepackage{float}

usepackage{caption}

usepackage{subcaption}

usepackage{wrapfig}

usepackage{amsmath}

usepackage{amssymb}

usepackage{physics}

usepackage{caption}



usepackage{tikz}

usetikzlibrary{decorations.markings}

usetikzlibrary{shapes,arrows}

usetikzlibrary{calc}

usetikzlibrary{arrows.meta}

usetikzlibrary{intersections,through,backgrounds}

usepackage{lipsum}  





usepackage[a4paper, left=2.5cm, right=2.5cm,

top=2.5cm, bottom=2.5cm]{geometry}  





begin{document}



section{Motivation and Notation}



begin{wrapfigure}{r}{0textwidth}

    vspace{-25cm}

    begin{tikzpicture}[rotate=90,scale=1.5]

    vspace{-5cm}

    hspace{0.3cm}

    foreach a/l in {0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$} { %a is the angle variable

        draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt); 

        node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) {l};

    }

    draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;





    node [label={[red,xshift=0.1cm, yshift=0.0cm]$p_2$}] (m1) at ($(a0)!0.65!(a300)$){};

    draw[->] (a0) -- (m1);



    node [label={[red,xshift=0.35cm, yshift=-0.2cm]$p_3$}] (m2) at ($(a300)!0.65!(a240)$){};

    draw[->] (a300) -- (m2);



    node [label={[red,xshift=0.5cm, yshift=-0.5cm]$p_4$}] (m3) at ($(a240)!0.65!(a180)$){};

    draw[->] (a240) -- (m3);



    node [label={[red,xshift=0.15cm, yshift=-0.8cm]$p_5$}] (m4) at ($(a180)!0.65!(a120)$){};

    draw[->] (a180) -- (m4);



    node [label={[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$}] (m5) at ($(a120)!0.65!(a60)$){};

    draw[->] (a120) -- (m5);



    node [label={[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$}] (m6) at ($(a60)!0.65!(a0)$){};

    draw[->] (a60) -- (m6);

    end{tikzpicture}

    setlength{belowcaptionskip}{-5pt}

    captionsetup{justification=centering,margin=5cm}

    vspace*{-5cm}

    hspace{0.5cm}

    caption{A $n$ = 6 representation of $p$-conservation, where the momenta $p^{mu}$ form a closed contour in dual space.}

    label{fig:Diagram_Mom_Con}

end{wrapfigure}



lipsum[1-4] 











end{document}

The easiest to move a wrapfig up is to change intextsep, as it is used also at the bottom, you must insert a rule there to compensate. The drawback is that it moves the text at the side down. One can use vspace{-2cm} there to compensate.

documentclass{article}

usepackage{wrapfig,graphicx,tikz,caption}

usetikzlibrary{calc}

begin{document}

section{Motivation and Notation}



setlengthintextsep{-3cm}

begin{wrapfigure}{r}{0textwidth}

    begin{tikzpicture}[rotate=90,scale=1.5]

    foreach a/l in {0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$} { %a is the angle variable

        draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt);

        node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) {l};

    }

    draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;





    node [label={[red,xshift=0.1cm, yshift=0.0cm]$p_2$}] (m1) at ($(a0)!0.65!(a300)$){};

    draw[->] (a0) -- (m1);



    node [label={[red,xshift=0.35cm, yshift=-0.2cm]$p_3$}] (m2) at ($(a300)!0.65!(a240)$){};

    draw[->] (a300) -- (m2);



    node [label={[red,xshift=0.5cm, yshift=-0.5cm]$p_4$}] (m3) at ($(a240)!0.65!(a180)$){};

    draw[->] (a240) -- (m3);



    node [label={[red,xshift=0.15cm, yshift=-0.8cm]$p_5$}] (m4) at ($(a180)!0.65!(a120)$){};

    draw[->] (a180) -- (m4);



    node [label={[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$}] (m5) at ($(a120)!0.65!(a60)$){};

    draw[->] (a120) -- (m5);



    node [label={[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$}] (m6) at ($(a60)!0.65!(a0)$){};

    draw[->] (a60) -- (m6);

    end{tikzpicture}

    setlength{belowcaptionskip}{-5pt}

    captionsetup{justification=centering,margin=5cm}

    caption{A $n$ = 6 representation of $p$-conservation, where the momenta $p^{mu}$ form a closed contour in dual space.}

    label{fig:Diagram_Mom_Con}

    rule{0pt}{3.0cm}

end{wrapfigure}



We have described the spinor-helicity formalism as a natural way to encode massless scattering amplitudes. However, we have to impose momentum conservation by hand, since spinor-helicity is derived from a Lorentz invariant foundation, which can be thought of as a subgroup of Poincar'e invariance. The 10-dimensional Poincar'e group includes translations (3 spatial and 1 time) as well as the 6-dimensional Lorentz group, consisting of 3 boosts and 3 rotations. Hence, spinor variables are not invariant under spatial translations, and momentum is not automatically conserved footnotemark.

Since all scattering processes naturally conserve momentum, we would like to have a formalism where both the on-shell massless condition, $p^2 =0$ and momentum conservation, $sum p^{mu} = 0$ are manifest. This comes in the form of momentum twistors, developed by Hodges as an extension of Penrose's twistor geometry.



footnotetext{This is a well-known consequence of Noether's Theorem. See REFS REMOVED For more explicit details.}



%

par

We take inspiration by considering a different geometrical interpretation of momentum conservation. We start by drawing an $n$-sided polygon in dual space, as shown by Figure ref{fig:Diagram_Mom_Con}.

There are two ways to consider defining the polygon; either through the edges or the vertices. Considering the edges, we obtain the traditional statement of momentum conservation; the $n$ edges form a closed contour, which corresponds to the net sum of momenta equalling zero, and no new intuition has been obtained.

par

Let us now define the polygon through the vertices, using a new set of dual coordinates $x_i$ where $i={ 1,dots,n}$. To ensure our contour is closed, we demand the periodic boundary $x_{0} equiv x_{n}$. The momenta in dual space may now be defined as the difference of these dual coordinates





end{document}

Another possiblity is to use a raisebox and to hide the height from the wrapfig. You must then also set the baseline of the tikzpicture to the north.

documentclass{article}

usepackage{wrapfig,graphicx,tikz,caption,lipsum}

usetikzlibrary{calc}

begin{document}

section{Motivation and Notation}



begin{wrapfigure}{r}{0textwidth}

raisebox{1cm}[0pt]{%

begin{tikzpicture}[rotate=90,scale=1.5,baseline=(current bounding box.north)]

    foreach a/l in {0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$} { %a is the angle variable

        draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt);

        node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) {l};

    }

    draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;





    node [label={[red,xshift=0.1cm, yshift=0.0cm]$p_2$}] (m1) at ($(a0)!0.65!(a300)$){};

    draw[->] (a0) -- (m1);



    node [label={[red,xshift=0.35cm, yshift=-0.2cm]$p_3$}] (m2) at ($(a300)!0.65!(a240)$){};

    draw[->] (a300) -- (m2);



    node [label={[red,xshift=0.5cm, yshift=-0.5cm]$p_4$}] (m3) at ($(a240)!0.65!(a180)$){};

    draw[->] (a240) -- (m3);



    node [label={[red,xshift=0.15cm, yshift=-0.8cm]$p_5$}] (m4) at ($(a180)!0.65!(a120)$){};

    draw[->] (a180) -- (m4);



    node [label={[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$}] (m5) at ($(a120)!0.65!(a60)$){};

    draw[->] (a120) -- (m5);



    node [label={[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$}] (m6) at ($(a60)!0.65!(a0)$){};

    draw[->] (a60) -- (m6);

    end{tikzpicture}}

caption{bbb}

end{wrapfigure}

We have described the spinor-helicity formalism as a natural way to encode massless scattering amplitudes. However, we have to impose momentum conservation by hand, since spinor-helicity is derived from a Lorentz invariant foundation, which can be thought of as a subgroup of Poincar'e invariance. The 10-dimensional Poincar'e group includes translations (3 spatial and 1 time) as well as the 6-dimensional Lorentz group, consisting of 3 boosts and 3 rotations. Hence, spinor variables are not invariant under spatial translations, and momentum is not automatically conserved footnotemark.

Since all scattering processes naturally conserve momentum, we would like to have a formalism where both the on-shell massless condition, $p^2 =0$ and momentum conservation, $sum p^{mu} = 0$ are manifest. This comes in the form of momentum twistors, developed by Hodges as an extension of Penrose's twistor geometry.



footnotetext{This is a well-known consequence of Noether's Theorem. See REFS REMOVED For more explicit details.}



%

par

We take inspiration by considering a different geometrical interpretation of momentum conservation. We start by drawing an $n$-sided polygon in dual space, as shown by Figure ref{fig:Diagram_Mom_Con}.

There are two ways to consider defining the polygon; either through the edges or the vertices. Considering the edges, we obtain the traditional statement of momentum conservation; the $n$ edges form a closed contour, which corresponds to the net sum of momenta equalling zero, and no new intuition has been obtained.

par

Let us now define the polygon through the vertices, using a new set of dual coordinates $x_i$ where $i={ 1,dots,n}$. To ensure our contour is closed, we demand the periodic boundary $x_{0} equiv x_{n}$. The momenta in dual space may now be defined as the difference of these dual coordinates





end{document}

The conceivably easiest way to move the tikzpicture up is to adjust its bounding box. All I did was to add

path[use as bounding box] (-3,-3) rectangle (3,2);

(and to do the rotate in a scope because otherwise it is confusing) to get

documentclass[12pt,a4paper,twoside]{report}

usepackage{float}

usepackage{caption}

usepackage{subcaption}

usepackage{wrapfig}

usepackage{amsmath}

usepackage{amssymb}

usepackage{caption}



usepackage{tikz}

usetikzlibrary{decorations.markings}

usetikzlibrary{shapes,arrows}

usetikzlibrary{calc}

usetikzlibrary{arrows.meta}

usetikzlibrary{intersections,through,backgrounds}

usepackage{lipsum}  





usepackage[a4paper, left=2.5cm, right=2.5cm,

top=2.5cm, bottom=2.5cm]{geometry}  





begin{document}



section{Motivation and Notation}



begin{wrapfigure}{r}{0textwidth}

    begin{tikzpicture}

    path[use as bounding box] (-3,-3) rectangle (3,2);

    begin{scope}[rotate=90,scale=1.5]

    foreach a/l in {0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$} { %a is the angle variable

        draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt); 

        node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) {l};

    }

    draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;





    node [label={[red,xshift=0.1cm, yshift=0.0cm]$p_2$}] (m1) at ($(a0)!0.65!(a300)$){};

    draw[->] (a0) -- (m1);



    node [label={[red,xshift=0.35cm, yshift=-0.2cm]$p_3$}] (m2) at ($(a300)!0.65!(a240)$){};

    draw[->] (a300) -- (m2);



    node [label={[red,xshift=0.5cm, yshift=-0.5cm]$p_4$}] (m3) at ($(a240)!0.65!(a180)$){};

    draw[->] (a240) -- (m3);



    node [label={[red,xshift=0.15cm, yshift=-0.8cm]$p_5$}] (m4) at ($(a180)!0.65!(a120)$){};

    draw[->] (a180) -- (m4);



    node [label={[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$}] (m5) at ($(a120)!0.65!(a60)$){};

    draw[->] (a120) -- (m5);



    node [label={[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$}] (m6) at ($(a60)!0.65!(a0)$){};

    draw[->] (a60) -- (m6);

    end{scope}

    end{tikzpicture}

    setlength{belowcaptionskip}{-5pt}

    captionsetup{justification=centering,margin=5cm}

    vspace*{-5cm}

    hspace{0.5cm}

    caption{A $n$ = 6 representation of $p$-conservation, where the momenta $p^{mu}$ form a closed contour in dual space.}

    label{fig:Diagram_Mom_Con}

end{wrapfigure}



lipsum[1-4] 



end{document}

Or with

 path[use as bounding box] (-3,-3) rectangle (3,1);